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首页> 外文期刊>Circuits and Systems I: Regular Papers, IEEE Transactions on >A Unified Approach to Chaos Suppressing and Inducing in a Periodically Forced Family of Nonlinear Oscillators
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A Unified Approach to Chaos Suppressing and Inducing in a Periodically Forced Family of Nonlinear Oscillators

机译：周期强迫非线性振荡器族中混沌抑制和感应的统一方法

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This paper finds and investigates the application of single-exponential local decay pulse (SELDP) to suppress and induce chaos in a family of nonlinear oscillators subject to weak damping and external periodic excitations. Fourier series of SELDP defined on a period is derived and the approximate series is extended to that defined on the set of whole positive real numbers. To show the feasibility of the obtained results, we first give an effective design scheme of electrical circuit related to SELDP signal and this may be helpful in future implementations. We concentrate on this case in which the unforced system possesses two homoclinic orbits. In order to apply Melnikov's approach to make the underlying parameter conditions for suppressing and inducing chaos more clear, a generic numerical algorithm is proposed to compute complicated Melnikov functions. Two propositions, serving as designing the correct parameters in the SELDP function are also given. From our study, we find that chaos can be induced (suppressed) according to the corresponding Melnikov functions have (do not have) simple zeros. Our work can help to understand the underlying mechanisms of suppressing and inducing chaos. The simulation results show the effectiveness of our proposed approach.
机译：本文发现并研究了单指数局部衰减脉冲（SELDP）在抑制弱阻尼和外部周期性激励的非线性振荡器族中抑制和诱发混沌的应用。得出在周期上定义的SELDP的傅里叶级数，并将近似级数扩展到在整个正实数集上定义的级数。为了说明所获得结果的可行性，我们首先给出一种与SELDP信号相关的有效电路设计方案，这可能对将来的实现有所帮助。我们专注于这种情况，其中无力系统拥有两个同斜轨道。为了应用梅尔尼科夫方法使抑制和诱导混沌的基本参数条件更加清晰，提出了一种通用的数值算法来计算复杂的梅尔尼科夫函数。还给出了两个命题，即设计SELDP函数中的正确参数。从我们的研究中，我们发现，可以根据相应的Melnikov函数具有（不具有）简单零来诱发（抑制）混沌。我们的工作可以帮助您了解抑制和诱发混乱的潜在机制。仿真结果表明了该方法的有效性。

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