Amplitude death in oscillators coupled by a one-way ring time-delay connection.
Amplitude death in oscillators coupled by a one-way ring time-delay connection.
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DOI：
10.1103/physreve.70.066201
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发表时间：
2004-12
期刊：
影响因子：
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通讯作者：
K. Konishi
中科院分区：
文献类型：
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作者：
K. Konishi
在由扩散连接耦合的相同非线性振子中，不能观察到稳态的耦合诱导稳定化，称为振幅死亡。然而，分析证实，使用扩散时延耦合可以引起振幅死亡。本文提出了一种由N个同振子组成的单环时延耦合系统。当N=1时，该系统相当于一个延迟反馈控制系统，当N=2时，该系统相当于一个时滞耦合振荡器系统。在该系统中，当雅可比矩阵在不动点处的值为奇数个实正特征值时，在稳定状态下不会发生振幅死亡。此外，还给出了一个简单的系统图形程序来测试系统的稳定性。这个过程是在两个数值例子说明：耦合Rössler振子和耦合洛伦兹振子。
The coupling induced stabilization of a steady state, which is called amplitude death, cannot be observed in identical nonlinear oscillators coupled by diffusive connections. However, it has been analytically confirmed that amplitude death can be induced by using a diffusive time-delay coupling. In this paper, a one-way ring time-delay coupled system consisting of N identical oscillators is proposed. This system is equivalent to a delayed-feedback control system when N=1, and to a time-delay coupled oscillator system when N=2. In the proposed system, amplitude death never occurs at a steady state when the Jacobi matrix evaluated at a fixed point has an odd number of real positive eigenvalues. Furthermore, a simple systematic graphical procedure to test the stability of the system is presented. This procedure is illustrated in two numerical examples: coupled Rössler oscillators and coupled Lorenz oscillators.