中国物理B ›› 1993, Vol. 2 ›› Issue (8): 561-568.doi: 10.1088/1004-423X/2/8/001

• GENERAL •    下一篇

THE SECOND-ORDER APPROXIMATION OF THRESHOLD VALUE OF CHAOS

苏景辉   

  1. Department of physics, Harbin Shipbuilding Engineering Institute, Harbin 150001, China
  • 收稿日期:1992-07-16 出版日期:1993-08-20 发布日期:1993-08-20

THE SECOND-ORDER APPROXIMATION OF THRESHOLD VALUE OF CHAOS

SU JING-HUI (苏景辉)   

  1. Department of physics, Harbin Shipbuilding Engineering Institute, Harbin 150001, China
  • Received:1992-07-16 Online:1993-08-20 Published:1993-08-20

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摘要： For the Melnikov theory of chaos, the second-order approximation is given. Applying the result to the dynamics system with quadratic nonlinear term, it is shown that the threshold of chaos depends on initial condition and can be greater than that of the Melnikov method. The first order variational equations of some nonlinear dynamical systems are all the second-order ordinary differential equations with hyperbolic cosine function, its solution is given.

Abstract: For the Melnikov theory of chaos, the second-order approximation is given. Applying the result to the dynamics system with quadratic nonlinear term, it is shown that the threshold of chaos depends on initial condition and can be greater than that of the Melnikov method. The first order variational equations of some nonlinear dynamical systems are all the second-order ordinary differential equations with hyperbolic cosine function, its solution is given.

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
02.30.Hq (Ordinary differential equations) 02.30.Jr (Partial differential equations)