Shilnikov sense chaos in a simple three-dimensional system  

作　　者：王炜 张琪昌 田瑞兰 

机构地区：[1]Department of Mechanics,School of Mechanical Engineering,Tianjin University [2]Centre for Nonlinear Dynamics Research,Shijiazhuang Railway Institute

出　　处：《Chinese Physics B》2010年第3期207-216,共10页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant No. 10872141)

摘　　要：The Shilnikov sense Smale horseshoe chaos in a simple 3D nonlinear system is studied. The proportional integral derivative （PID） controller is improved by introducing the quadratic and cubic nonlinearities into the governing equa- tions. For the discussion of chaos, the bifurcate parameter value is selected in a reasonable regime at the requirement of the Shilnikov theorem. The analytic expression of the Shilnikov type homoclinic orbit is accomplished. It depends on the series form of the manifolds surrounding the saddle-focus equilibrium. Then the methodology is extended to research the dynamical behaviours of the simplified solar-wind-driven-magnetosphere-ionosphere system. As is illustrated, the Lyapunov characteristic exponent spectra of the two systems indicate the existence of chaotic attractor under some specific parameter conditions.The Shilnikov sense Smale horseshoe chaos in a simple 3D nonlinear system is studied. The proportional integral derivative （PID） controller is improved by introducing the quadratic and cubic nonlinearities into the governing equa- tions. For the discussion of chaos, the bifurcate parameter value is selected in a reasonable regime at the requirement of the Shilnikov theorem. The analytic expression of the Shilnikov type homoclinic orbit is accomplished. It depends on the series form of the manifolds surrounding the saddle-focus equilibrium. Then the methodology is extended to research the dynamical behaviours of the simplified solar-wind-driven-magnetosphere-ionosphere system. As is illustrated, the Lyapunov characteristic exponent spectra of the two systems indicate the existence of chaotic attractor under some specific parameter conditions.

关 键 词：CHAOS Shilnikov theorem homoclinic orbit MANIFOLD 

分 类 号：O415.5[理学—理论物理] O175.13[理学—物理]