A Giant Chaotic Network Based on Hyperchaotic Parallel Series Network

Abstract

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.