Coexistence of multiple attractors and crisis route to chaos in autonomous third order Duffing-Holmes type chaotic oscillators
Coexistence of multiple attractors and crisis route to chaos in autonomous third order Duffing-Holmes type chaotic oscillators
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DOI：
10.1016/j.cnsns.2015.11.009
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发表时间：
2016-07
期刊：
影响因子：
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通讯作者：
J. Kengne;Z. Njitacke;H. Fotsin
中科院分区：
文献类型：
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作者：
J. Kengne;Z. Njitacke;H. Fotsin
我们对Tamasevicius等人（2009）最近提出的一个由自治三阶Duffing-Holmes型混沌振子组成的系统进行了系统的分析。在这种类型的振荡器中，通过使用一对反并联连接的半导体二极管来合成产生混沌振荡所需的非线性分量的对称特性。基于肖克利二极管方程和明智的选择状态变量，我们推导出一个光滑的数学模型（包括双曲正弦和余弦函数），更好地描述了经常和混沌动力学的振荡器。分岔分析表明，混沌是通过经典的倍周期和对称性恢复危机方案实现的。更有趣的是，发现了参数空间中对应于多个吸引子共存的一些区域（例如，对于相同的系统参数值，四个不同的吸引子共存）。这种惊人的现象是独一无二的，以前在电路（包括通用蔡氏电路，尽管有大量的相关研究工作）中还没有报道过，因此对理解一般非线性动力系统的行为做出了有意义的贡献。对该振子的非线性动力学进行了PSpice仿真，验证了理论分析的正确性。
We perform a systematic analysis of a system consisting of an autonomous third order Duffing–Holmes type chaotic oscillator recently introduced by Tamasevicius et al. (2009). In this type of oscillators, the symmetrical characteristics of the nonlinear component necessary for generating chaotic oscillations is synthesized by using a pair of semiconductor diodes connected in anti-parallel. Based on the Shockley diode equation and a judicious choice of state variables, we derive a smooth mathematical model (involving hyperbolic sine and cosine functions) for a better description of both the regular and chaotic dynamics of the oscillator. The bifurcation analysis shows that chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. More interestingly, some regions of the parameter space corresponding to the coexistence of multiple attractors (e.g. coexistence of four different attractors for the same values of system parameters) are discovered. This striking phenomenon is unique and has not yet been reported previously in an electrical circuit (the universal Chua's circuit included, in spite the immense amount of related research work), and thus represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. Some PSpice simulations of the nonlinear dynamics of the oscillator are carried out to verify the theoretical analysis.