随机振子网络中的扩散诱导不稳定性和混沌
Diffusion-induced instability and chaos in random oscillator networks
摘要：
我们证明了随机网络上的扩散耦合极限环振子可以表现出各种复杂的动力学模式。减少系统的网络模拟复杂的金斯堡-朗道方程，我们认为，均匀振荡可以是线性不稳定的自发相位调制由于扩散耦合-在连续介质中的本杰明-Feir不稳定性的效果。在随机无标度网络中，这种不稳定性下的数值研究揭示了大量复杂的动力学机制，包括部分振幅死亡、聚类和混沌。本文建立了一个解释各种非线性动力学的动力学平均场论.
英文摘要：
We demonstrate that diffusively coupled limit-cycle oscillators on random networks can exhibit various complex dynamical patterns. Reducing the system to a network analog of the complex Ginzburg-Landau equation, we argue that uniform oscillations can be linearly unstable with respect to spontaneous phase modulations due to diffusional coupling - the effect corresponding to the Benjamin-Feir instability in continuous media. Numerical investigations under this instability in random scale-free networks reveal a wealth of complex dynamical regimes, including partial amplitude death, clustering, and chaos. A dynamic mean-field theory explaining different kinds of nonlinear dynamics is constructed.
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