Bursting Dynamics in a Singular Vector Field with Codimension Three Triple Zero Bifurcation
Bursting Dynamics in a Singular Vector Field with Codimension Three Triple Zero Bifurcation
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DOI：
10.3390/math11112486
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发表时间：
2023-05
期刊：
影响因子：
2.4
通讯作者：
Weipeng Lyu;Shaolong Li;Zhenyang Chen;Qinsheng Bi
中科院分区：
文献类型：
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作者：
Weipeng Lyu;Shaolong Li;Zhenyang Chen;Qinsheng Bi
多时间尺度非线性系统作为一种具有特殊非线性结构的动力系统，是当前非线性动力学理论发展的重要方向之一。实际应用中的多时间尺度非线性系统往往是高维和高协维特征耦合的复杂形式，导致系统中各种复杂的爆破振荡行为和分岔特征。为了研究高余维分岔引起的复杂爆破动力学问题，本文考虑了具有三零分岔的矢量场的范式。在双参数平面上讨论了两种可能导致复杂爆破振荡的余维2分岔。基于快慢分析方法，引入慢变量W=Asin(ωt)，研究了系统运动轨迹随W变化的演化过程，揭示了几种爆破振荡的动力机理。最后，通过改变慢变量的频率，推导出了一类由倍周期级联引起的混沌爆破现象。开展相关工作，对于深入认识各种复杂爆破现象的本质，加强力学、数学等基础学科在工程实践中的应用，起到了积极的作用。
As a kind of dynamical system with a particular nonlinear structure, a multi-time scale nonlinear system is one of the essential directions of the current development of nonlinear dynamics theory. Multi-time scale nonlinear systems in practical applications are often complex forms of coupling of high-dimensional and high codimension characteristics, leading to various complex bursting oscillation behaviors and bifurcation characteristics in the system. For exploring the complex bursting dynamics caused by high codimension bifurcation, this paper considers the normal form of the vector field with triple zero bifurcation. Two kinds of codimension-2 bifurcation that may lead to complex bursting oscillations are discussed in the two-parameter plane. Based on the fast–slow analysis method, by introducing the slow variable W=Asin(ωt), the evolution process of the motion trajectory of the system changing with W was investigated, and the dynamical mechanism of several types of bursting oscillations was revealed. Finally, by varying the frequency of the slow variable, a class of chaotic bursting phenomena caused by the period-doubling cascade is deduced. Developing related work has played a positive role in deeply understanding the nature of various complex bursting phenomena and strengthening the application of basic disciplines such as mechanics and mathematics in engineering practice.