{"id":9404,"date":"2024-03-02T10:28:31","date_gmt":"2024-03-02T10:28:31","guid":{"rendered":"https:\/\/www.hnjournal.net\/?page_id=9404"},"modified":"2024-03-02T10:28:35","modified_gmt":"2024-03-02T10:28:35","slug":"5-3-6","status":"publish","type":"page","link":"https:\/\/www.hnjournal.net\/ar\/5-3-6\/","title":{"rendered":"\u0646\u0638\u0627\u0645 \u0631\u0628\u0627\u0639\u064a \u0627\u0644\u0627\u0628\u0639\u0627\u062f \u0645\u0634\u062a\u0642 \u0645\u0646 \u0646\u0638\u0627\u0645 Sprott-B"},"content":{"rendered":"

\u0627\u062d\u0645\u062f \u0630\u0646\u0648\u0646 \u0634\u064a\u062a1<\/sup><\/strong><\/p>\n

1<\/sup> \u0645\u062f\u0631\u0633 \u0641\u064a \u0648\u0632\u0627\u0631\u0629 \u0627\u0644\u062a\u0631\u0628\u064a\u0629 \u0627\u0644\u0639\u0631\u0627\u0642\u064a\u0629.<\/p>\n

\u0628\u0631\u064a\u062f \u0627\u0644\u0643\u062a\u0631\u0648\u0646\u064a: ahmed.20csp139@student.uomosul.edu.iq<\/p>\n

HNSJ, 2024, 5(3); https:\/\/doi.org\/10.53796\/hnsj53\/6<\/p>\n

\u062a\u0646\u0632\u064a\u0644 \u0627\u0644\u0645\u0644\u0641<\/a><\/p>\n

\u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0646\u0634\u0631: 01\/03\/2024\u0645 \u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0642\u0628\u0648\u0644: 08\/02\/2024\u0645<\/p>\n

\u0627\u0644\u0645\u0633\u062a\u062e\u0644\u0635 <\/strong><\/p>\n

\u062a\u0645 \u0628\u0646\u0627\u0621 \u0646\u0638\u0627\u0645 \u062c\u062f\u064a\u062f \u0631\u0628\u0627\u0639\u064a \u0627\u0644\u0627\u0628\u0639\u0627\u062f (4D) \u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628 \u0645\u0639 \u0646\u0642\u0637\u062a\u064a \u0627\u062a\u0632\u0627\u0646 \u063a\u064a\u0631 \u0645\u0633\u062a\u0642\u0631\u0629, \u0648\u0630\u0644\u0643 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0646 \u0628\u064a\u0646 \u0646\u0638\u0627\u0645 Sprott-B\u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0627\u0628\u0639\u0627\u062f \u0648\u0646\u0638\u0627\u0645 \u062e\u0637\u064a \u0630\u064a \u0628\u0639\u062f \u0648\u0627\u062d\u062f (1D) \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0633\u062a\u0631\u0627\u062a\u064a\u062c\u064a\u0629 \u0627\u0642\u062a\u0631\u0627\u0646 (Coupling strategy). \u0628\u0627\u0644\u0645\u0642\u0627\u0631\u0646\u0629 \u0645\u0639 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062a\u0642\u0644\u064a\u062f\u064a\u0629\u060c \u064a\u0639\u062a\u0628\u0631 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062c\u062f\u064a\u062f \u0628\u0633\u064a\u0637\u064b\u0627 \u0644\u0623\u0646\u0647 \u064a\u062a\u0643\u0648\u0646 \u0645\u0646 \u0633\u0628\u0639\u0629 \u062d\u062f\u0648\u062f \u0645\u0639 \u062d\u062f\u064a\u0646 \u063a\u064a\u0631 \u062e\u0637\u064a\u064a\u0646. \u0646\u0638\u0631\u064b\u0627 \u0644\u0637\u0628\u064a\u0639\u0629 \u0646\u0642\u0627\u0637 \u0627\u0644\u0627\u062a\u0632\u0627\u0646\u060c \u064a\u0646\u062a\u0645\u064a \u0647\u0630\u0627 \u0627\u0644\u0646\u0638\u0627\u0645 \u0625\u0644\u0649 \u0641\u0626\u0629 \u0627\u0644\u062c\u0648\u0627\u0630\u0628 \u0627\u0644\u0645\u062a\u062d\u0641\u0632\u0629 \u0630\u0627\u062a\u064a\u064b\u0627 (Self-excited). \u0623\u062e\u064a\u0631\u064b\u0627, \u062a\u0651\u0645\u062a \u062f\u0631\u0627\u0633\u0629 \u0645\u0633\u0623\u0644\u0629 \u0627\u0644\u062a\u0632\u0627\u0645\u0646 (Synchronization) \u0644\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0645\u0642\u062a\u0631\u062d \u0645\u0646 \u062e\u0644\u0627\u0644 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0648\u0623\u0638\u0647\u0631\u062a \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0645\u0648\u0627\u0641\u0642\u062a\u0647\u0627 \u0645\u0639 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0646\u0638\u0631\u064a\u0629.<\/p>\n

\u0627\u0644\u0643\u0644\u0645\u0627\u062a \u0627\u0644\u0645\u0641\u062a\u0627\u062d\u064a\u0629: <\/strong>\u0623\u0633\u064a\u0627\u062a Lyapunov (LEs), \u0645\u062a\u062d\u0641\u0632\u0629 \u0630\u0627\u062a\u064a\u064b\u0627, \u0646\u0638\u0627\u0645 Sprott-B, \u0627\u0644\u062a\u0632\u0627\u0645\u0646.<\/p>\n

<\/a>Research title <\/strong><\/p>\n

The 4D system is derived from the Sprott-B system<\/strong><\/p>\n

Ahmed T. Sheet1<\/sup><\/strong><\/p>\n

1<\/sup> Teacher at the Iraqi Ministry of Education<\/p>\n

Email: ahmed.20csp139@student.uomosul.edu.iq<\/p>\n

HNSJ, 2024, 5(3); https:\/\/doi.org\/10.53796\/hnsj53\/6<\/p>\n

Published at 01\/03\/2024 Accepted at 08\/02\/2024 <\/strong><\/p>\n

Abstract <\/strong><\/p>\n

A new highly disordered four-dimensional (4D) system with two unstable equilibrium points was built by coupling a three-dimensional Sprott-B system with a one-dimensional (1D) linear system using a coupling strategy. Compared with traditional systems, the new system is simple because it consists of seven terms with two nonlinear terms. Due to the nature of the equilibrium points, this system belongs to the class of self-excited attractors. Finally, the issue of synchronization of the proposed system was studied through stability theory, and numerical simulation showed agreement with theoretical results.<\/p>\n

    \n
  1. \u0627\u0644\u0645\u0642\u062f\u0645\u0629<\/strong><\/li>\n<\/ol>\n

    \u0627\u0643\u062a\u0633\u0628 \u062a\u0632\u0627\u0645\u0646 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u063a\u064a\u0631 \u0627\u0644\u062e\u0637\u064a\u0629 \u0627\u0644\u0645\u062a\u0635\u0644\u0629 \u0639\u0628\u0631 \u0634\u0628\u0643\u0627\u062a \u0648\u0627\u0633\u0639\u0629 \u0627\u0644\u0646\u0637\u0627\u0642 \u0634\u0639\u0628\u064a\u0629 \u0641\u064a \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u062a\u0646\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a\u060c \u0645\u062b\u0644 \u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0637\u0627\u0642\u0629 \u0648\u0634\u0628\u0643\u0627\u062a \u0627\u0644\u0627\u0633\u062a\u0634\u0639\u0627\u0631 \u0648\u0639\u0644\u0645 \u0627\u0644\u0623\u062d\u064a\u0627\u0621. \u0641\u064a \u0639\u0627\u0645 1990 \u060c \u0642\u062f\u0645 \u0643\u0644 \u0645\u0646 Pecora \u0648 Carroll \u0623\u0646\u0638\u0645\u0629 \u0630\u0627\u062a \u062c\u0648\u0627\u0630\u0628 \u0645\u062a\u062d\u0641\u0632\u0629 \u0630\u0627\u062a\u064a\u0627 \u062d\u064a\u062b \u062a\u0639\u062a\u0628\u0631 \u0627\u0644\u0638\u0627\u0647\u0631\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 \u0641\u064a \u062a\u0632\u0627\u0645\u0646 \u0627\u0644\u0641\u0648\u0636\u0649 [1] \u0627\u0644\u062a\u064a \u062d\u0638\u064a\u062a \u0628\u0627\u0647\u062a\u0645\u0627\u0645 \u0643\u0628\u064a\u0631 \u0641\u064a \u0645\u062e\u062a\u0644\u0641 \u0627\u0644\u0645\u062c\u0627\u0644\u0627\u062a \u0645\u062b\u0644 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 [2] \u0648\u0627\u0644\u062a\u0631\u0645\u064a\u0632 [3] \u0648\u0645\u062c\u0627\u0644\u0627\u062a \u0623\u062e\u0631\u0649. \u064a\u062a\u0645 \u0648\u0635\u0641 \u0627\u0644\u062a\u0632\u0627\u0645\u0646 \u0627\u0644\u0643\u0627\u0645\u0644 (Complete (synchronization \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0643\u0627\u0641\u0624 \u0646\u0645\u0648 \u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u0627\u0644\u0629 \u0628\u0645\u0631\u0648\u0631 \u0627\u0644\u0648\u0642\u062a. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0623\u064a\u0627\u0645\u060c \u064a\u0633\u062a\u062e\u062f\u0645 \u0645\u0639\u0638\u0645 \u0639\u0644\u0645\u0627\u0621 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0648\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621 \u0648\u0627\u0644\u0645\u0647\u0646\u062f\u0633\u064a\u0646 \u0637\u0631\u064a\u0642\u0629 Lyapunov \u0627\u0644\u062b\u0627\u0646\u064a\u0629 \u0643\u0623\u062f\u0627\u0629 \u0631\u0626\u064a\u0633\u064a\u0629 \u0641\u064a \u0623\u0639\u0645\u0627\u0644\u0647\u0645 \u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a\u0629 [4].<\/p>\n

    \u064a\u0634\u064a\u0631 \u0647\u0630\u0627 \u0627\u0644\u0628\u062d\u062b \u0628\u0634\u0643\u0644 \u0623\u0633\u0627\u0633\u064a \u0625\u0644\u0649 \u0623\u0646 \u0627\u0644\u062a\u0632\u0627\u0645\u0646 \u0627\u0644\u0641\u0648\u0636\u0648\u064a \u0644\u0646\u0638\u0627\u0645 \u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628 \u0627\u0644\u062c\u062f\u064a\u062f \u0627\u0644\u0630\u064a \u0642\u062f\u0645\u0647 Sprott \u0643\u0634\u0641 \u0639\u0646 \u062a\u0633\u0639\u0629 \u0639\u0634\u0631 \u0646\u0638\u0627\u0645\u064b\u0627 [5] \u0628\u0645\u0627 \u0641\u064a \u0630\u0644\u0643 \u0646\u0638\u0627\u0645 Sprott-B \u0627\u0644\u0645\u0639\u0631\u0648\u0641\u060c \u062d\u064a\u062b \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 LEs \u0628\u062d\u064a\u062b \u064a\u0643\u0648\u0646 \u0623\u0643\u0628\u0631 \u0639\u0646\u0635\u0631 \u0645\u0648\u062c\u0628 \u0645\u0646 LEs \u0647\u0648 0.2169 \u0648\u0647\u0648 \u0623\u0643\u0628\u0631 \u0645\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0623\u0635\u0644\u064a\u060c \u0645\u0645\u0627 \u0634\u062c\u0639\u0646\u0627 \u0639\u0644\u0649 \u062a\u0643\u0648\u064a\u0646 \u0646\u0638\u0627\u0645 \u062c\u062f\u064a\u062f \u0647\u0648 \u0623\u0646\u0646\u0627 \u062a\u0645\u0643\u0646\u0627 \u0645\u0646 \u062a\u0643\u0648\u064a\u0646 \u0646\u0638\u0627\u0645 \u064a\u062d\u062a\u0648\u064a 7 \u062d\u062f\u0648\u062f\u060c \u0648 \u064a\u0639\u062a\u0628\u0631 \u0623\u0628\u0633\u0637 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u0646\u0648\u0639, \u0647\u0630\u0627 \u0647\u0648 \u0623\u062d\u062f \u0634\u0631\u0648\u0637 \u062a\u0643\u0648\u064a\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062a\u064a \u0630\u0643\u0631\u0647\u0627 Sprott [6]. \u0627\u0644\u062c\u062f\u0648\u0644 )1( \u064a\u0644\u062e\u0635 \u0628\u0639\u0636 \u0623\u0646\u0638\u0645\u0629 4D \u0627\u0644\u0645\u062a\u0627\u062d\u0629\u060c \u0648\u064a\u0631\u0643\u0632 \u0639\u0644\u0649 \u0623\u0647\u0645 \u0627\u0644\u062e\u0635\u0627\u0626\u0635\u060c \u0628\u0645\u0627 \u0641\u064a \u0630\u0644\u0643 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0625\u062c\u0645\u0627\u0644\u064a \u0644\u0644\u062d\u062f\u0648\u062f\u060c \u0648\u0622\u0633\u064a\u0629 Lyapunov \u0648 \u0643\u0630\u0644\u0643 \u0633\u0644\u0648\u0643 \u0627\u0644\u062c\u0648\u0627\u0630\u0628.<\/p>\n

    \u062c\u062f\u0648\u0644 (1)<\/strong> \u0645\u0644\u062e\u0635 \u062a\u0635\u0646\u064a\u0641\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629 \u0644\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0641\u0648\u0636\u0649 4D.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
    \u0627\u0644\u062a\u0633\u0644\u0633\u0644<\/td>\n\u0633\u0644\u0648\u0643 \u0627\u0644\u0646\u0638\u0627\u0645<\/td>\n<\/td>\n\u0639\u062f\u062f \u0627\u0644\u062d\u062f\u0648\u062f<\/td>\n\u0633\u0644\u0648\u0643 \u0627\u0644\u062c\u0648\u0627\u0630\u0628<\/td>\n\u0627\u0644\u0645\u0635\u062f\u0631<\/td>\n<\/tr>\n
    <\/td>\n\u0641\u0648\u0636\u0649<\/strong><\/td>\n<\/td>\n10<\/td>\n\u0645\u062e\u0641\u064a\u0629<\/td>\n[7]<\/td>\n<\/tr>\n
    <\/td>\n\u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628<\/strong><\/td>\n<\/td>\n9<\/td>\n\u0645\u062e\u0641\u064a\u0629<\/td>\n[8]<\/td>\n<\/tr>\n
    <\/td>\n\u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628<\/strong><\/td>\n<\/td>\n9<\/td>\n\u0645\u062a\u062d\u0641\u0632\u0629 \u0630\u0627\u062a\u064a\u0627\u064b<\/td>\n[9]<\/td>\n<\/tr>\n
    <\/td>\n\u0641\u0648\u0636\u0649<\/strong><\/td>\n<\/td>\n10<\/td>\n\u0645\u062e\u0641\u064a\u0629<\/td>\n[10]<\/td>\n<\/tr>\n
    <\/td>\n\u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628<\/strong><\/td>\n<\/td>\n11<\/td>\n\u0645\u062a\u062d\u0641\u0632\u0629 \u0630\u0627\u062a\u064a\u0627\u064b<\/td>\n[11]<\/td>\n<\/tr>\n
    <\/td>\n\u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628<\/strong><\/td>\n<\/td>\n12<\/td>\n\u0645\u062a\u062d\u0641\u0632\u0629 \u0630\u0627\u062a\u064a\u0627\u064b<\/td>\n[12]<\/td>\n<\/tr>\n
    <\/td>\n\u0641\u0648\u0636\u0649<\/strong><\/td>\n<\/td>\n8<\/td>\n\u0645\u062e\u0641\u064a\u0629<\/td>\n[13]<\/td>\n<\/tr>\n
    <\/td>\n\u0641\u0648\u0636\u0649<\/strong><\/td>\n<\/td>\n8<\/td>\n\u0645\u062e\u0641\u064a\u0629<\/td>\n[14]<\/td>\n<\/tr>\n
    <\/td>\n\u0641\u0648\u0636\u0649<\/strong><\/td>\n<\/td>\n8<\/td>\n\u0645\u062e\u0641\u064a\u0629<\/td>\n[15]<\/td>\n<\/tr>\n
    <\/td>\n\u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628<\/strong><\/td>\n<\/td>\n9<\/td>\n\u0645\u062a\u062d\u0641\u0632\u0629 \u0630\u0627\u062a\u064a\u0627\u064b<\/td>\n[16]<\/td>\n<\/tr>\n
    <\/td>\n\u0641\u0648\u0636\u0649<\/strong><\/td>\n<\/td>\n9<\/td>\n\u0645\u062e\u0641\u064a\u0629<\/td>\n[17]<\/td>\n<\/tr>\n
    <\/td>\n\u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628<\/strong><\/td>\n<\/td>\n7<\/td>\n\u0645\u062a\u062d\u0641\u0632\u0629 \u0630\u0627\u062a\u064a\u0627\u064b<\/td>\n\u0647\u0630\u0627 \u0627\u0644\u0639\u0645\u0644<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
      \n
    1. \u0648\u0635\u0641 \u0627\u0644\u0646\u0638\u0627\u0645<\/strong><\/li>\n<\/ol>\n

      \u0644\u0625\u0646\u0634\u0627\u0621 \u0623\u0646\u0638\u0645\u0629 \u062c\u062f\u064a\u062f\u0629 \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0645\u062a\u0648\u0641\u0631\u0629 \u0633\u0627\u0628\u0642\u064b\u0627\u060c \u064a\u0645\u0643\u0646 \u0623\u0646 \u0646\u0633\u062a\u062e\u062f\u0645 \u0633\u064a\u0637\u0631\u0629 \u0627\u0644\u062a\u063a\u0630\u064a\u0629 \u0627\u0644\u0631\u0627\u062c\u0639\u0629 (State feedback controller) \u0648\u0627\u0633\u062a\u0631\u0627\u062a\u064a\u062c\u064a\u0629 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0646 (Coupling strategies). \u062a\u062a\u0637\u0644\u0628 \u0627\u0644\u0625\u0633\u062a\u0631\u0627\u062a\u064a\u062c\u064a\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 \u0625\u062f\u062e\u0627\u0644 \u0645\u062a\u063a\u064a\u0631 \u062c\u062f\u064a\u062f \u0641\u064a \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0623\u0635\u0644\u064a \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629. \u0628\u064a\u0646\u0645\u0627 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0627\u0633\u062a\u0631\u0627\u062a\u064a\u062c\u064a\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629\u060c \u0647\u0646\u0627\u0643 \u062d\u0627\u062c\u0629 \u0641\u0642\u0637 \u0625\u0644\u0649 \u0627\u0644\u062c\u0645\u0639 \u0628\u064a\u0646 \u0646\u0638\u0627\u0645\u064a\u0646 \u0645\u062e\u062a\u0644\u0641\u064a\u0646.<\/p>\n

      \u0641\u064a \u0639\u0627\u0645 1994 \u0627\u0643\u062a\u0634\u0641 \u0627\u0644\u0628\u0627\u062d\u062b Sprott \u062a\u0633\u0639\u0629 \u0639\u0634\u0631 \u0646\u0638\u0627\u0645\u0627 \u062a\u062a\u0645\u064a\u0632 \u0628\u0628\u0633\u0627\u0637\u062a\u0647\u0627. \u064a\u064f\u0639\u0631\u064e\u0651\u0641 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0641\u0648\u0636\u0648\u064a \u062b\u0644\u0627\u062b\u064a \u0627\u0644\u0623\u0628\u0639\u0627\u062f Sprott-B \u0628\u0623\u0646\u0647 [5]:<\/p>\n

      (1)<\/p>\n

      \u0645\u0646 \u0627\u0644\u0648\u0627\u0636\u062d \u0623\u0646 \u0647\u0630\u0627 \u0627\u0644\u0646\u0638\u0627\u0645 \u064a\u062a\u0643\u0648\u0646 \u0645\u0646 \u062e\u0645\u0633\u0629 \u062d\u062f\u0648\u062f \u0641\u0642\u0637 \u0645\u0639 \u0622\u0633\u064a\u0629 Lyapunov \u0645\u0648\u062c\u0628\u0629 \u0648\u0627\u062d\u062f\u0629<\/p>\n

      \u0648\u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n

      \u0648\u0623\u0643\u0628\u0631 \u0623\u0633 \u064a\u0633\u0627\u0648\u064a . \u0627\u0633\u062a\u0646\u0627\u062f\u064b\u0627 \u0625\u0644\u0649 \u0625\u0633\u062a\u0631\u0627\u062a\u064a\u062c\u064a\u0629 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0646 \u0648\u0627\u0644\u0646\u0638\u0627\u0645 \u0623\u0639\u0644\u0627\u0647\u060c \u064a\u062a\u0645 \u0625\u0636\u0627\u0641\u0629 \u0646\u0638\u0627\u0645 D1 \u0630\u064a \u062d\u062f\u064a\u0646 \u062e\u0637\u064a\u064a\u0646 \u0628\u0645\u0627 \u0641\u064a \u0630\u0644\u0643 \u0645\u0639\u0644\u0645\u0629 \u0627\u0642\u062a\u0631\u0627\u0646 \u0625\u0644\u0649 \u0627\u0644\u0646\u0638\u0627\u0645 (1)\u060c \u0648\u0627\u0644\u0630\u064a \u064a\u0646\u062a\u062c \u0646\u0638\u0627\u0645\u064b\u0627 \u0628\u0633\u064a\u0637\u064b\u0627 \u062c\u062f\u064a\u062f\u064b\u0627 Sprott-B\u0631\u0628\u0627\u0639\u064a \u0627\u0644\u0627\u0628\u0639\u0627\u062f \u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628, \u064a\u062a\u0645 \u062a\u0642\u062f\u064a\u0645\u0647 \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n

      (2)<\/p>\n

      \u0627\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062c\u062f\u064a\u062f (2) \u064a\u062a\u0643\u0648\u0646 \u0645\u0646 \u0633\u0628\u0639\u0629 \u062d\u062f\u0648\u062f \u0645\u0646 \u0636\u0645\u0646\u0647\u0627 \u0627\u062b\u0646\u0627\u0646 \u063a\u064a\u0631 \u062e\u0637\u064a\u0629. \u0643\u0645\u0627 \u0627\u0646\u0647 \u0646\u0638\u0627\u0645 \u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628 (Hyperchaotic), \u064a\u0645\u062a\u0644\u0643 \u0646\u0642\u0637\u062a\u064a \u0627\u062a\u0632\u0627\u0646 \u0630\u0648\u0627\u062a \u062c\u0648\u0627\u0630\u0628 \u0645\u062a\u062d\u0641\u0632\u0629 \u0630\u0627\u062a\u064a\u0627 \u0639\u0646\u062f \u0645\u0639 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \u0648\u0639\u0646\u062f \u0645\u0639 , \u0643\u0645\u0627 \u0645\u0648\u0636\u062d \u0641\u064a \u0627\u0644\u0634\u0643\u0644 (1).<\/p>\n

      \"G:\\4D\\b=1\\\u0627\u0644\u0631\u0633\u0645\\3D\\untitled.tif\" \"C:\\Users\\Hp\\Desktop\\\u0628\u062f\u0644\u0647b=1.tif\"<\/p>\n

      \u0627\u0644\u0634\u0643\u0644 (1)<\/em><\/strong> \u062c\u0648\u0627\u0630\u0628 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0645\u062a\u0648\u0644\u062f \u0645\u0639 \u0641\u064a \u0627\u0644\u0645\u0633\u062a\u0648\u064a (<\/em>a): , \u0641\u064a \u0641\u0636\u0627\u0621 \u0627\u0644\u0637\u0648\u0631(<\/em>b): .<\/em><\/p>\n

        \n
      1. \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0646\u0638\u0627\u0645<\/strong><\/li>\n<\/ol>\n

        \u064a\u062a\u0645 \u062a\u062d\u0644\u064a\u0644 \u0628\u0639\u0636 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062c\u062f\u064a\u062f (2) \u0646\u0638\u0631\u064a\u064b\u0627 \u0648\u0639\u062f\u062f\u064a\u064b\u0627\u060c \u0623\u064a \u0646\u0642\u0627\u0637 \u0627\u0644\u0627\u062a\u0632\u0627\u0646 \u0648\u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631\u064a\u0629 \u0648 \u0622\u0633\u064a\u0629 Lyapunov \u0648\u0628\u064f\u0639\u062f Kaplan-Yorke.<\/p>\n

          \n
        • \u0646\u0642\u0627\u0637 \u0627\u0644\u0627\u062a\u0632\u0627\u0646 \u0648 \u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631\u064a\u0629<\/em><\/strong> (Equilibrium Points and Stability)<\/li>\n<\/ul>\n

          \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c \u0648\u062a\u062d\u062f\u064a\u062f\u0627\u064b \u0641\u064a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629\u060c \u062a\u0639\u062a\u0628\u0631 \u0646\u0642\u0627\u0637 \u0627\u0644\u0627\u062a\u0632\u0627\u0646 \u062d\u0644\u0627\u064b \u062b\u0627\u0628\u062a\u064b\u0627 \u0644\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629. \u0644\u0625\u064a\u062c\u0627\u062f \u0646\u0642\u0627\u0637 \u0627\u0644\u0627\u062a\u0632\u0627\u0646 \u0644\u0644\u0646\u0638\u0627\u0645 (2)\u060c \u0646\u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n

          (3)<\/p>\n

          \u0641\u0627\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0645\u062a\u0648\u0644\u062f \u064a\u0645\u062a\u0644\u0643 \u0646\u0642\u0637\u062a\u064a \u0627\u062a\u0632\u0627\u0646 \u0645\u062a\u0646\u0627\u0638\u0631\u062a\u064a\u0646 \u0647\u0645\u0627 \u0648<\/p>\n

          . \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 (Jacobian matrix) \u0639\u0646\u062f \u0648 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0645\u0645\u064a\u0632\u0629 (Characteristic equation) \u0644\u0644\u0646\u0638\u0627\u0645 (2) \u064a\u062a\u0645 \u0639\u0631\u0636\u0647\u0645 \u0628\u0627\u0644\u062a\u0648\u0627\u0644\u064a \u0639\u0644\u0649 \u0627\u0644\u0646\u062d\u0648 \u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n

          (4)<\/p>\n

          (5)<\/p>\n

          \u0627\u0645\u0627 \u0623\u062b\u0631 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 )4) \u0641\u064a\u062d\u0633\u0628 \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n

          \u0628\u0645\u0627 \u0627\u0646\u0647 \u0623\u062b\u0631 (), \u0641\u0625\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u064a\u0643\u0648\u0646 \u0645\u062d\u0627\u0641\u0638\u0627\u064b (<\/em>Conservative).<\/em><\/p>\n

          \u0644\u062a\u062d\u062f\u064a\u062f \u0627\u0633\u062a\u0642\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629<\/em> (2) \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0639\u064a\u0627\u0631<\/em> Routh-Hurwitz [18],<\/p>\n

          \u062d\u064a\u062b , \u0648 \u0628\u0630\u0644\u0643 \u062a\u0643\u0648\u0646 \u0627\u0630\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0645\u062a\u0648\u0644\u062f (2) \u063a\u064a\u0631 \u0645\u0633\u062a\u0642\u0631 (Unstable) \u0648\u0628\u0630\u0644\u0643 \u064a\u0635\u0646\u0641 \u0630\u0627 \u062c\u0648\u0627\u0630\u0628 \u0645\u062a\u062d\u0641\u0632\u0629 \u0630\u0627\u062a\u064a\u0627 (Self-excited) \u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628 (Hyperchaotic).<\/p>\n

          \u0645\u0644\u0627\u062d\u0638\u0629: <\/em><\/strong>\u0639\u0646\u062f \u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 (5) \u0646\u062d\u0635\u0644 \u0639\u0644\u0649<\/p>\n

          \u0648\u0628\u0630\u0644\u0643 \u0627\u0644\u0646\u0642\u0627\u0637 \u062a\u0635\u0628\u062d Saddle-focus [5].<\/p>\n

            \n
          • \u0622\u0633\u064a\u0629<\/em> \u0644\u064a\u0627\u0628\u0648\u0646\u0648\u0641<\/em> <\/strong>(Lyapunov Exponent)<\/li>\n<\/ul>\n

            \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0645\u0639\u0644\u0645\u0629 \u0648 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \u0641\u0623\u0646 \u0622\u0633\u064a\u0629 <\/em>Lyapunov \u0644\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062c\u062f\u064a\u062f (2) \u0647\u064a:<\/p>\n

            (6)<\/p>\n

            \u0646\u0644\u0627\u062d\u0638 \u0623\u0646 \u0627\u0643\u0628\u0631 \u0622\u0633\u064a\u0629 <\/em>Lyapunov \u0644\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062c\u062f\u064a\u062f (2) \u0647\u064a \u0648\u0628\u0630\u0644\u0643 \u062a\u0643\u0648\u0646 \u0627\u0643\u0628\u0631 \u0645\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0627\u0635\u0644\u064a (1), , \u0645\u0645\u0627 \u064a\u062f\u0644 \u0639\u0644\u0649 \u0627\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062c\u062f\u064a\u062f \u0627\u0643\u062b\u0631 \u0643\u0641\u0627\u0621\u0629 \u0645\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0627\u0635\u0644\u064a<\/em> [19], \u0643\u0645\u0627 \u0625\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062c\u062f\u064a\u062f \u064a\u0645\u062a\u0644\u0643 \u0627\u0644\u0633\u0645\u0629 \u0627\u062b\u0646\u062a\u0627\u0646 \u0645\u0646 \u0622\u0633\u064a\u0629 <\/em>Lyapunov \u0627\u0644\u0645\u0648\u062c\u0628\u0629 \u0643\u0645\u0627 \u0645\u0648\u0636\u062d \u0641\u064a \u0627\u0644\u0634\u0643\u0644 (2).<\/p>\n

            \"G:\\4D\\b=1\\\u0627\u0633\u064a\u0629<\/em><\/p>\n

            \u0627\u0644\u0634\u0643\u0644 (2)<\/em><\/strong> \u0622\u0633\u064a\u0629 <\/em>Lyapunov \u0644\u0644\u0646\u0638\u0627\u0645 (<\/em>2) \u0639\u0646\u062f \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 <\/em><\/p>\n

            \u0643\u0630\u0644\u0643 \u0645\u062c\u0645\u0648\u0639 \u0622\u0633\u064a\u0629 <\/em>Lyapunov \u0648 \u0628\u0645\u0627 \u0627\u0646\u0647 , \u0627\u0630\u0646 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0645\u062a\u0637\u0627\u0628\u0642\u0629 \u0645\u0639 \u0627\u0644\u062d\u0644\u0648\u0644 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 (<\/em>Wolf\u2019s Algorithm).<\/em><\/p>\n

            \u0648 \u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u0628\u0639\u062f <\/em>Lyapunov (\u0628\u0639\u062f <\/em>Kaplan-Yorke) \u0644\u0644\u0646\u0638\u0627\u0645 (2) \u0647\u0648:<\/p>\n

            \u0645\u0646 \u062e\u0644\u0627\u0644 \u0628\u0631\u0646\u0627\u0645\u062c Wolf\u2019s algorithm \u0641\u0627\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0645\u062a\u0648\u0644\u062f \u062f\u0627\u0626\u0645\u0627 \u064a\u0643\u0648\u0646 \u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628 \u062a\u062d\u062a \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \u0648 \u0627\u0644\u062c\u062f\u0648\u0644 (2) \u064a\u0639\u0631\u0636 \u0647\u0630\u0627 \u0627\u0644\u0633\u0644\u0648\u0643 \u0645\u0639 \u0642\u064a\u0645 \u0645\u062e\u062a\u0644\u0641\u0629 \u0644\u0644\u0645\u0639\u0644\u0645\u0629 .<\/p>\n

            \u062c\u062f\u0648\u0644 (2)<\/strong> \u0644\u0644\u0646\u0638\u0627\u0645 (2) \u0645\u0639 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \u0648\u0642\u064a\u0645 \u0645\u062e\u062a\u0644\u0641\u0629 \u0644\u0644\u0645\u0639\u0644\u0645\u0629 .<\/p>\n\n\n\n\n\n\n\n\n\n
            <\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n\u0627\u0634\u0627\u0631\u0627\u062a<\/td>\n\u0627\u0644\u0633\u0644\u0648\u0643<\/td>\n\u0627\u0644\u062a\u0633\u0644\u0633\u0644<\/td>\n<\/tr>\n
            0.3<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n\u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628<\/td>\n<\/td>\n<\/tr>\n
            0.09<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n<\/td>\n\u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628<\/td>\n<\/td>\n<\/tr>\n
            0.58<\/td>\n1.0016<\/td>\n0.2135<\/td>\n0.0002-<\/td>\n1.2149-<\/td>\n<\/td>\n\u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628<\/td>\n<\/td>\n<\/tr>\n
            0.587<\/td>\n1.0017<\/td>\n0.2097<\/td>\n0.0000<\/td>\n1.2115-<\/td>\n<\/td>\n\u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628<\/td>\n<\/td>\n<\/tr>\n
            0.619<\/td>\n1.0019<\/td>\n0.2232<\/td>\n0.0000<\/td>\n1.2251-<\/td>\n<\/td>\n\u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628<\/td>\n<\/td>\n<\/tr>\n
            0.914<\/td>\n1.0031<\/td>\n10.214<\/td>\n0.0003<\/td>\n1.2175-<\/td>\n<\/td>\n\u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
              \n
            1. \u0633\u0644\u0648\u0643 \u0627\u0644\u062a\u0639\u0627\u064a\u0634 <\/em>(Coexistence of attractors)<\/strong><\/li>\n<\/ol>\n

              \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0641\u0636\u0627\u0621 \u0627\u0644\u0637\u0648\u0631, \u0641\u0623\u0646 \u062c\u0648\u0627\u0630\u0628 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0645\u062a\u0648\u0644\u062f \u062a\u062a\u0645\u062b\u0644 \u0641\u064a \u0627\u0644\u0634\u0643\u0644 (3) \u062a\u062d\u062a \u0646\u0641\u0633 \u0627\u0644\u0645\u0639\u0644\u0645\u0629 \u0648 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629, \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u0648\u0644\u0649 \u0628\u0627\u0644\u0644\u0648\u0646 \u0627\u0644\u0623\u062d\u0645\u0631 \u0648 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629 \u0648 \u0628\u0627\u0644\u0644\u0648\u0646 \u0627\u0644\u0627\u0632\u0631\u0642. \u0648 \u0627\u0644\u0634\u0643\u0644 (4) \u062a\u062d\u062a \u0627\u0644\u0645\u0639\u0644\u0645\u0629 \u0645\u0639 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629, \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u0648\u0644\u0649 (\u0623\u062d\u0645\u0631) \u0648 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u062b\u0627\u0646\u064a\u0629 (\u0627\u0632\u0631\u0642).<\/em><\/p>\n

              \"G:\\4D\\b=1\\multistability\\a=0.01\\\u0628\u062f\u0648\u0646<\/em><\/p>\n

              \u0627\u0644\u0634\u0643\u0644 (3)<\/strong> \u0627\u0644\u0641\u0636\u0627\u0621 x-z-w, \u0627\u0644\u062a\u0639\u0627\u064a\u0634 \u0644\u062c\u0627\u0630\u0628\u064a\u0646 \u0645\u0639 \u0648\u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629 (\u0623\u062d\u0645\u0631) \u0648 (\u0627\u0632\u0631\u0642).<\/p>\n

              \"G:\\4D\\b=1\\multistability\\a=4.1\\\u0628\u062f\u0648\u0646<\/p>\n

              \u0627\u0644\u0634\u0643\u0644 (4)<\/strong> \u0627\u0644\u0641\u0636\u0627\u0621 x-y-z, \u0627\u0644\u062a\u0639\u0627\u064a\u0634 \u0644\u062c\u0627\u0630\u0628\u064a\u0646 \u0645\u0639 \u0648\u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \u0627\u0644\u0645\u062a\u0646\u0627\u0638\u0631\u0629 (\u0623\u062d\u0645\u0631) \u0648 (\u0627\u0632\u0631\u0642).<\/p>\n

                \n
              1. \u0627\u0644\u062a\u0632\u0627\u0645\u0646 \u0627\u0644\u0643\u0627\u0645\u0644 (synchronization Complete)<\/strong><\/li>\n<\/ol>\n

                \u064a\u0645\u0643\u0646 \u062a\u0639\u0631\u064a\u0641 \u0646\u0638\u0627\u0645\u064a \u0627\u0644\u0642\u064a\u0627\u062f\u0629 (<\/em>Drive) \u0648 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 (<\/em>Response) \u0644\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062c\u062f\u064a\u062f (2) \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u062a\u064a\u0646 (7) \u0648 (8),\u0639\u0644\u0649 \u0627\u0644\u062a\u0648\u0627\u0644\u064a:<\/em><\/p>\n

                (7)<\/p>\n

                (8)<\/p>\n

                \u0648 \u0646\u0639\u0631\u0641 \u062e\u0637\u0623 \u0627\u0644\u062a\u0632\u0627\u0645\u0646 (Synchronization error) \u0628\u064a\u0646 \u0627\u0644\u0646\u0638\u0627\u0645\u064a\u0646 (7) \u0648 (8) \u0643\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n

                (9)<\/p>\n

                \u064a\u0637\u0644\u0642 \u0639\u0644\u0649 \u0647\u0630\u0627 \u0627\u0644\u062a\u0632\u0627\u0645\u0646 \u0628\u0627\u0644\u062a\u0632\u0627\u0645\u0646 \u0627\u0644\u0643\u0627\u0645\u0644, \u062d\u064a\u062b \u0627\u0646 \u0647\u064a \u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0642\u064a\u0627\u0633 \u0648 \u0627\u0646<\/em><\/p>\n

                \u0648\u0628\u0630\u0644\u0643 \u0641\u0625\u0646 \u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0642\u064a\u0627\u0633 \u0647\u064a \u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0648\u062d\u062f\u0629.<\/em><\/p>\n

                \u0628\u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 (9) \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u062e\u0637\u0627 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062f\u064a\u0646\u0627\u0645\u064a\u0643\u064a \u0628\u064a\u0646 \u0627\u0644\u0646\u0638\u0627\u0645\u064a\u0646 <\/em>(7) \u0648 (8) \u0641\u064a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 (10).<\/em><\/p>\n

                (10)<\/p>\n

                \u0648 \u0644\u062a\u062d\u0642\u064a\u0642 \u0627\u0644\u062a\u0632\u0627\u0645\u0646 \u064a\u062c\u0628 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0634\u0631\u0637 \u0627\u0644\u062a\u0627\u0644\u064a:<\/em><\/p>\n

                (11)<\/p>\n

                \u0645\u0628\u0631\u0647\u0646\u0629:<\/strong> \u0625\u0630 \u062a\u0645 \u062a\u0635\u0645\u064a\u0645 \u0648\u062d\u062f\u0629 \u0627\u0644\u0633\u064a\u0637\u0631\u0629 (Controller) \u0643\u0627\u0644\u062a\u0627\u0644\u064a:<\/p>\n

                (12)<\/p>\n

                \u0641\u0627\u0646 \u0646\u0638\u0627\u0645 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 \u064a\u062a\u0628\u0639 \u0646\u0638\u0627\u0645 \u0627\u0644\u0642\u064a\u0627\u062f\u0629<\/em>.<\/p>\n

                \u0627\u0644\u0628\u0631\u0647\u0627\u0646 :<\/em><\/strong> \u0628\u062a\u0639\u0648\u064a\u0636 \u0627\u0644\u0633\u064a\u0637\u0631\u0629 (12) \u0641\u064a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 (10), \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:<\/em><\/p>\n

                (13)<\/p>\n

                \u0648 \u0628\u0627\u062e\u062a\u064a\u0627\u0631 \u062f\u0627\u0644\u0629 Lyapunov \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:<\/p>\n

                (14)<\/p>\n

                \u0648 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 (14) \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0632\u0645\u0646 \u062a\u0643\u0648\u0646:<\/em><\/p>\n

                \n

                \n

                (15)<\/p>\n

                \u062d\u064a\u062b \u064a\u0624\u062f\u064a \u0627\u0644\u0649 . \u0643\u0645\u0627 \u0627\u0646 \u0639\u0644\u0649 . \u0627\u0644\u0633\u064a\u0637\u0631\u0629 (12) \u064a\u062d\u0642\u0642 \u0639\u062f\u062f\u064a\u0627 \u0627\u0644\u062a\u0632\u0627\u0645\u0646 \u0627\u0644\u0643\u0627\u0645\u0644 <\/em>(<\/em><\/strong>synchronization Complete). <\/em><\/strong>\u0643\u0645\u0627 \u0645\u0648\u0636\u062d \u0641\u064a \u0627\u0644\u0634\u0643\u0644\u064a\u0646 (5) \u0648 (6), \u0627\u0644\u062a\u0632\u0627\u0645\u0646 \u0627\u0644\u0643\u0627\u0645\u0644 \u0627\u0644\u062d\u0627\u0635\u0644 \u0628\u064a\u0646 \u0627\u0644\u0646\u0638\u0627\u0645\u064a\u0646 (7) \u0648 (8) \u0645\u0639 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0627\u0628\u062a\u062f\u0627\u0626\u064a\u0629 \u0648 , \u0648\u0647\u0630\u0627 \u064a\u0624\u0643\u062f \u0635\u062d\u0629 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0646\u0638\u0631\u064a\u0629.<\/em><\/p>\n

                \"G:\\4D\\b=1\\\u0628\u0631\u0627\u0645\u062c<\/p>\n

                \u0627\u0644\u0634\u0643\u0644 (5)<\/em><\/strong> \u062e\u0637\u0623 \u0627\u0644\u062a\u0632\u0627\u0645\u0646 (<\/em>Synchronization error) \u0645\u0639 \u0627\u0644\u0633\u064a\u0637\u0631\u0629 (12).<\/em><\/p>\n

                \"G:\\4D\\b=1\\\u0628\u0631\u0627\u0645\u062c<\/p>\n

                \u0627\u0644\u0634\u0643\u0644 (13.2) <\/strong>\u0627\u0644\u062a\u0632\u0627\u0645\u0646 \u0627\u0644\u0643\u0627\u0645\u0644 (The complete synchronization).<\/p>\n

                  \n
                1. \u0627\u0644\u0645\u0633\u062a\u062e\u0644\u0635 <\/strong><\/li>\n<\/ol>\n

                  \u0628\u0627\u0644\u0627\u0639\u062a\u0645\u0627\u062f \u0639\u0644\u0649 \u0646\u0638\u0627\u0645 Sprott-B \u0627\u0644\u0645\u0639\u0631\u0648\u0641 \u0648\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0627\u0642\u062a\u0631\u0627\u0646\u060c \u062a\u0645 \u062a\u0642\u062f\u064a\u0645 \u0646\u0638\u0627\u0645 \u062c\u062f\u064a\u062f \u0628\u0633\u064a\u0637 \u0634\u062f\u064a\u062f \u0627\u0644\u0627\u0636\u0637\u0631\u0627\u0628 \u0631\u0628\u0627\u0639\u064a \u0627\u0644\u0623\u0628\u0639\u0627\u062f \u0645\u0639 \u0633\u0628\u0639\u0629 \u062d\u062f\u0648\u062f. \u064a\u062d\u062a\u0648\u064a \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0645\u0642\u062a\u0631\u062d \u0639\u0644\u0649 \u0646\u0642\u0637\u062a\u064a \u0627\u062a\u0632\u0627\u0646 \u063a\u064a\u0631 \u0645\u0633\u062a\u0642\u0631\u062a\u064a\u0646 \u0648\u064a\u0646\u062a\u0645\u064a\u0627\u0646 \u0625\u0644\u0649 \u0641\u0626\u0629 \u0627\u0644\u062c\u0648\u0627\u0630\u0628 \u0627\u0644\u0645\u062a\u062d\u0641\u0632\u0629 \u0630\u0627\u062a\u064a\u064b\u0627\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0623\u0646\u0647 \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0645\u064a\u0632\u0629 (n-2) \u0645\u0646 \u0622\u0633\u064a\u0629 Lyapunov \u0627\u0644\u0645\u0648\u062c\u0628\u0629\u060c \u0648 \u0623\u0643\u0628\u0631 \u0623\u0633 Lyapunov \u0627\u0644\u062a\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0647\u064a \u0623\u0643\u0628\u0631 \u0645\u0646 \u0627\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u0623\u0635\u0644\u064a. \u0646\u0639\u062a\u0642\u062f \u0623\u0646 \u0627\u0644\u0639\u0645\u0644 \u0627\u0644\u0628\u062d\u062b\u064a \u064a\u062c\u0628 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0645\u0641\u064a\u062f\u064b\u0627 \u0648\u064a\u0645\u0643\u0646 \u062a\u0639\u064a\u064a\u0646\u0647 \u0644\u0644\u0645\u0633\u0627\u0647\u0645\u0629 \u0641\u064a \u0627\u0644\u0645\u0624\u0644\u0641\u0627\u062a \u0627\u0644\u0639\u0644\u0645\u064a\u0629 \u062d\u0648\u0644 \u0637\u0631\u0642 \u0627\u0644\u0645\u0632\u0627\u0645\u0646\u0629 \u0627\u0644\u0643\u0627\u0645\u0644\u0629 \u0627\u0644\u062a\u064a \u0642\u062f \u064a\u0643\u0648\u0646 \u0644\u0647\u0627 \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0641\u064a \u0645\u062e\u062a\u0644\u0641 \u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u064a\u0629 \u0645\u0639 \u0627\u0644\u0627\u062a\u0635\u0627\u0644 \u0622\u0644\u0627\u0645\u0646.<\/p>\n

                  \u0627\u0644\u0645\u0635\u0627\u062f\u0631<\/strong><\/p>\n

                  [1] L. M. Pecora and T. L. Carroll, \u2018Synchronization of chaotic systems\u2019, Chaos<\/em>, vol. 25, no. 9, p. 097611, Sep. 2015, doi: 10.1063\/1.4917383.<\/p>\n

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