Vincent U E, Kenfack A, Njah A N, Akinlade O
Department of Physics, College of Natural Sciences, University of Agriculture, Abeokuta, Nigeria.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Nov;72(5 Pt 2):056213. doi: 10.1103/PhysRevE.72.056213. Epub 2005 Nov 17.
The bifurcation and chaotic behavior of unidirectionally coupled deterministic ratchets is studied as a function of the driving force amplitude and frequency . A classification of the various types of bifurcations likely to be encountered in this system was done by examining the stability of the steady state in linear response as well as constructing a two-parameter phase diagram in the plane. Numerical explorations revealed varieties of bifurcation sequences including quasiperiodic route to chaos. Besides, the familiar period-doubling and crises route to chaos exhibited by the one-dimensional ratchet were also found. In addition, the coupled ratchets display symmetry-breaking, saddle-nodes and bubbles of bifurcations. Chaotic behavior is characterized by using the Lyapunov exponent spectrum; while a perusal of the phase space projected in the Poincaré cross section confirms some of the striking features.
研究了单向耦合确定性棘轮的分岔和混沌行为与驱动力振幅和频率的关系。通过研究线性响应中稳态的稳定性以及构建平面上的双参数相图，对该系统中可能遇到的各种分岔类型进行了分类。数值探索揭示了包括准周期通向混沌路径在内的各种分岔序列。此外，还发现了一维棘轮所表现出的常见的倍周期和危机通向混沌路径。此外，耦合棘轮还表现出对称性破缺、鞍结和分岔气泡。利用李雅普诺夫指数谱对混沌行为进行了表征；而对庞加莱截面中投影的相空间的研读证实了一些显著特征。
