基于超混沌并行串联网络的巨混沌网络

S. Yan, Haijun Wang
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摘要

提出了一个具有巨大非线性混沌动力系统特征的巨大混沌网络。基于两个具有不同参数的空间耦合洛伦兹系统,采用超混沌能量源对每个混沌系统进行双向驱动。这就得到了一个具有两种方式的并联串联网络。双向网络中的每个节点都是一个高度非线性的动态系统,具有混沌特性,其中网络的每个节点都是一个混沌系统。然后,我们将这种网络定义为巨混沌网络或巨非线性混沌动力系统。我们通过李雅普诺夫指数图找到了许多超混沌状态及其超混沌区域。我们还给出了一个分岔图,大致说明了两个耦合洛伦兹系统从稳定状态到单周期状态、多周期状态、混沌状态和超混沌状态的动态行为。并通过最大LES讨论了各种状态同步差。该网络可以实现双向的超混沌同步和各节点的各种状态同步。本文的研究成果对人工网络、复杂系统和人工智能的研究具有重要意义。
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A Giant Chaotic Network Based on Hyperchaotic Parallel Series Network
We present a giant chaotic network having the characteristics of a giant nonlinear chaotic dynamic system. Based on two space coupling Lorentz systems with different parameters, a hyper-chaotic energy source is used to drive each chaotic system in two-way. Which results in a parallel series network with two ways. Each node in two-way of network is a highly nonlinear dynamic system and has the chaotic characteristics, where each node of network is a chaotic system. Then, we define such network as a giant chaotic network or a giant nonlinear chaotic dynamic system. We find many hyper-chaotic states and their hyper-chaotic regions via a Lyapunov exponents diagram. We also give a bifurcation diagram to illustrate roughly dynamic behavior of the two coupling Lorentz system from a stable state to a single-periodic state, a multi-periodic state, a chaotic state and a hyper-chaotic state by shifting some parameter. And we discuss all kinds of state synchronization difference via the maximal LES. The network can be found to obtain a hyper-chaotic synchronization and all kinds of state synchronizations in all nodes in two-way. Our research result is of great significance to the research of artificial network, complex system and artificial intelligence.
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