Pattern Formation in Networks of Nonlinear Systems with Delay Couplings
Pattern Formation in Networks of Nonlinear Systems with Delay Couplings
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DOI：
10.3182/20110828-6-it-1002.03773
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Eiichi Uchida;T. Oguchi
中科院分区：
文献类型：
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作者：
Eiichi Uchida;T. Oguchi
摘要本文研究了具有时滞的全同非线性系统网络的模式形成问题。首先，应用谐波平衡法，导出了具有时滞耦合的全同非线性系统网络的谐波平衡方程。然后，通过求解线性滞后系统的稳定性问题，我们可以估计耦合系统的振荡轮廓，如频率，振幅和相位。基于这种分析方法，我们还开发了一种设计方法的网络的非线性系统，可以实现一个指定的振荡剖面。数值算例表明了所提方法的有效性。
Abstract This paper considers pattern formation in networks of identical nonlinear systems with time-delays. First of all, applying the harmonic balance methods, we derive the corresponding harmonic balance equations for networks of identical nonlinear systems with delay couplings. Then, solving the equations by reducing to the stability problem of linear retarded systems, we can estimate the oscillation profile such as the frequency, amplitudes and phases of coupled systems. Based on this analysis method, we also develop a design method of networks of nonlinear systems that can achieve a prescribed oscillation profile. The effectiveness of the proposed methods is shown by numerical examples.