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Acta Physica Sinica (Overseas Edition), 1993, Vol. 2(8): 561-568    DOI: 10.1088/1004-423X/2/8/001
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THE SECOND-ORDER APPROXIMATION OF THRESHOLD VALUE OF CHAOS

SU JING-HUI (苏景辉)
Department of physics, Harbin Shipbuilding Engineering Institute, Harbin 150001, China
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.
Received:  16 July 1992      Accepted manuscript online: 
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  02.30.Hq (Ordinary differential equations)  
  02.30.Jr (Partial differential equations)  

Cite this article: 

SU JING-HUI (苏景辉) THE SECOND-ORDER APPROXIMATION OF THRESHOLD VALUE OF CHAOS 1993 Acta Physica Sinica (Overseas Edition) 2 561

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