On Universality of Transition to Chaos Scenario in Nonlinear Systems of Ordinary Differential Equations of Shilnikov’s Type  

作　　者：Maria Zaitseva Maria Zaitseva(Scientific Research Institute of System Development, Russian Academy of Science, Moscow, Russia;Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia)

机构地区：[1]Scientific Research Institute of System Development, Russian Academy of Science, Moscow, Russia [2]Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

出　　处：《Journal of Applied Mathematics and Physics》2016年第5期871-880,共10页应用数学与应用物理（英文）

摘　　要：Several nonlinear three-dimensional systems of ordinary differential equations are studied analytically and numerically in this paper in accordance with universal bifurcation theory of Feigenbaum-Sharkovskii-Magnitsky [1] [2]. All systems are autonomous and dissipative and display chaotic behaviour. The analysis confirms that transition to chaos in such systems is performed through cascades of bifurcations of regular attractors.Several nonlinear three-dimensional systems of ordinary differential equations are studied analytically and numerically in this paper in accordance with universal bifurcation theory of Feigenbaum-Sharkovskii-Magnitsky [1] [2]. All systems are autonomous and dissipative and display chaotic behaviour. The analysis confirms that transition to chaos in such systems is performed through cascades of bifurcations of regular attractors.

关 键 词：Nonlinear Differential Equations Dynamical Chaos Singular Attractor FSM-Theory 

分 类 号：O17[理学—数学]