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Resonant tori, transport barriers, and chaos in a vector field with a Neimark–Sacker bifurcation
Communications in Nonlinear Science and Numerical Simulation ( IF 3.9 ) Pub Date : 2020-02-12 , DOI: 10.1016/j.cnsns.2020.105226
Emmanuel Fleurantin , J.D. Mireles James

We make a detailed numerical study of a three dimensional dissipative vector field derived from the normal form for a cusp-Hopf bifurcation. The vector field exhibits a Neimark–Sacker bifurcation giving rise to an attracting invariant torus. Our main goals are to (A) follow the torus via parameter continuation from its appearance to its disappearance, studying its dynamics between these events, and to (B) study the embeddings of the stable/unstable manifolds of the hyperbolic equilibrium solutions over this parameter range, focusing on their role as transport barriers and their participation in global bifurcations. Taken together the results highlight the main features of the global dynamics of the system.



中文翻译:

Neimark–Sacker分叉的矢量场中的共振托里,传输壁垒和混沌

我们对源自尖顶-霍夫夫分支的正态形式的三维耗散向量场进行了详细的数值研究。向量场表现出Neimark-Sacker分叉,从而引起吸引不变的圆环。我们的主要目标是(A)通过从出现到消失的参数连续性来跟踪环面,研究这些事件之间的动力学,以及(B)研究该参数上双曲平衡解的稳定/不稳定流形的嵌入范围广泛,重点是它们作为运输障碍的作用以及它们在全球分支中的参与。综上所述,结果突出了系统全局动力学的主要特征。

更新日期:2020-02-12
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