Synchronization stability in Coupled oscillator Arrays: Solution for Arbitrary Configurations
Synchronization stability in Coupled oscillator Arrays: Solution for Arbitrary Configurations
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DOI：
10.1142/s0218127400000189
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发表时间：
2000-02
期刊：
影响因子：
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通讯作者：
L. Pecora;T. Carroll;G. Johnson;D. Mar;Kenneth S. Fink
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文献类型：
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作者：
L. Pecora;T. Carroll;G. Johnson;D. Mar;Kenneth S. Fink
当一组耦合振荡器处于相同的同步状态时，运动状态的稳定性往往是一个主要和关键的问题。当需要对许多不同结构的振荡器进行同步稳定时，这个问题的计算强度会变得很大。此外，通常没有关于如何根据需求更改配置以增强或降低稳定性的通用指导。我们最近引入了一个称为主稳定函数的概念，旨在实现两个目标：(1)减少计算同步稳定性的数值负载；(2)为设计符合所需稳定性的耦合配置提供指导。在此过程中，我们发展了相同同步问题的一个非常一般的公式，证明了在非常一般的情况下可以得到渐近结果，并证明了简单的振子组态可以探测到主稳定函数。
The stability of the state of motion in which a collection of coupled oscillators are in identical synchrony is often a primary and crucial issue. When synchronization stability is needed for many different configurations of the oscillators the problem can become computationally intense. In addition, there is often no general guidance on how to change a configuration to enhance or diminsh stability, depending on the requirements. We have recently introduced a concept called the Master Stability Function that is designed to accomplish two goals: (1) decrease the numerical load in calculating synchronization stability and (2) provide guidance in designing coupling configurations that conform to the stability required. In doing this, we develop a very general formulation of the identical synchronization problem, show that asymptotic results can be derived for very general cases, and demonstrate that simple oscillator configurations can probe the Master Stability Function.