离散混沌网络系统中共同噪声诱导同步的条件

噪声普遍存在于各种真实系统和人造系统中,它对系统的同步动力学具有多重影响.本文探索外部噪声对高维离散复杂网络系统同步行为的积极作用.首先构建外部共同噪声驱动下两个参数相同、未耦合的离散混沌网络模型,然后利用Birkhoff遍历定理与矩阵论等相关理论，严格证明了噪声诱导两个离散混沌网络系统取得同步的充分条件,进一步借助于具体的混沌网络模型,利用数值仿真验证了理论分析的有效性.数值模拟的结果表明当网络模型参数满足理论分析的充分条件时,共同噪声可以诱导两个参数相同、未耦合的离散混沌网络在随机意义下取得同步,而且同步效果不依赖于复杂网络拓扑结构的选取.

Condition of common noise induced synchronization in discrete chaotic network systems

Noise is ubiquitous in the various real and artificial systems, which plays multiple effects on synchronization of nonlinear systems. This study proposes to explore the positive influence of external common noise on the synchronous behavior of high dimensional discrete complex network. A network model of two uncoupled discrete chaotic networks with identical parameters under the excitation of external common noise is firstly constructed. By using the Birkhoff traversal theorem and the matrix theory, some sufficient conditions for synchronization of two discrete chaotic network systems are then proved. Meanwhile, by employing a specific chaotic network model, numerical simulation is used to verify the effectiveness of the theoretical analysis. The numerical results illustrate that when the parameters of network model meet the sufficient conditions for common noise induced synchronization, the two discrete chaotic networks can achieve synchronization in random sense. Moreover, the synchronization is robust against the variation of complex network topology. This paper obtains the theoretical conditions for common noise induced synchronization in the discrete chaotic networks for the first time, which not only can enrich the research of noise induced synchronization in some extent, but also can help to understand the positive effect of noise on ordered dynamics in high dimensional nonlinear chaotic systems.