Hopf bifurcation and chaos analysis of Chen’s system with distributed delays
Hopf bifurcation and chaos analysis of Chen’s system with distributed delays
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DOI：
10.1016/j.chaos.2004.11.007
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发表时间：
2005-07
影响因子：
7.8
通讯作者：
X. Liao;Guanrong Chen
中科院分区：
文献类型：
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作者：
X. Liao;Guanrong Chen
本文研究了一类具有分布时滞的非线性系统的一般模型。陈的系统可以由这个带有弱核的模型推导出来。在利用Routh-Hurwitz准则分析了局部稳定性之后，研究了Hopf分岔问题，利用范式理论和中心流形定理确定了分岔周期解的方向和稳定性。并给出了一些数值模拟来验证理论分析的正确性。通过数值模拟也发现了具有强核的Chen系统的混沌行为，给出了一些波形图、相图和分岔图并进行了分析。
In this paper, a general model of nonlinear systems with distributed delays is studied. Chen’s system can be derived from this model with the weak kernel. After the local stability is analyzed by using the Routh–Hurwitz criterion, Hopf bifurcation is studied, where the direction and the stability of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Some numerical simulations for justifying the theoretical analysis are also presented. Chaotic behavior of Chen’s system with the strong kernel is also found through numerical simulation, in which some waveform diagrams, phase portraits, and bifurcation plots are presented and analyzed.