Numerical bifurcation analysis framework for autonomous piecewise-smooth dynamical systems
Numerical bifurcation analysis framework for autonomous piecewise-smooth dynamical systems
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DOI：
10.1016/j.chaos.2008.11.013
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发表时间：
2009-10
影响因子：
7.8
通讯作者：
Q. Brandon;T. Ueta;D. Fournier-Prunaret;T. Kousaka
中科院分区：
文献类型：
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作者：
Q. Brandon;T. Ueta;D. Fournier-Prunaret;T. Kousaka
本文研究非线性分段光滑系统分支分析的一种数值方法。虽然线性分段光滑系统可以被严格分析，但非线性分段光滑系统不能导致解析解。从连续和离散系统的分析方法，我们的方法使用庞加莱映射的连续组件的部分分析的结果转化为从离散映射发出的。然后，我们应用传统的方法，以找到临界参数值，并获得在参数空间中的分岔图。数值计算的过程是充分描述和说明的各种版本的Alpazur振荡器的分析结果。
In this paper, we consider a numerical method for the bifurcation analysis method of nonlinear piecewise-smooth systems. While linear piecewise-smooth systems can be analyzed rigorously, nonlinear piecewise-smooth systems cannot lead to an analytical solution. Derived from both continuous and discrete system analysis approaches, our method uses a Poincaré map to transform the results of partial analysis over the continuous components into those issued from a discrete mapping. We then apply conventional methods in order to find critical parameter values and obtain bifurcation diagrams in the parameter space. The numerical procedure is fully described and illustrated by the analysis results of various versions of the Alpazur oscillator.