Feng Cun-Fang, Xu Xin-Jian, Wang Sheng-Jun, Wang Ying-Hai
Institute of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China.
Chaos. 2008 Jun;18(2):023117. doi: 10.1063/1.2912720.
We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed of a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks, and we find both its existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks.
我们研究随机网络上时滞混沌系统的投影超前、投影和投影滞后同步。我们放宽了先前工作的一些限制，在先前工作中，投影超前和投影滞后同步只能在两个耦合混沌系统上实现。在本文中，我们在由大量相互连接的组件组成的复杂动态网络上实现了投影超前和投影滞后同步。同时，尽管先前的工作研究了复杂动态网络上的投影同步，但节点的动力学是部分线性混沌系统。在本文中，复杂网络节点的动力学是时滞混沌系统，不受部分线性的限制。基于李雅普诺夫稳定性理论，我们提出了一种通用方法来实现随机动态网络上时滞混沌系统的投影超前、投影和投影滞后同步，并找到了其存在性和充分稳定性条件。通过在厄多斯 - 雷尼网络上使用池田和麦基 - 格拉斯系统检验具体示例，证明并验证了所提方法的有效性。
