Abstract
We first study how to make use of the Marotto theory to prove rigorously the existence of the Li‐Yorke chaos in diffusively coupled map lattices with open boundary conditions (i.e., a high‐dimensional discrete dynamical system). Then, the recent 0‐1 test for chaos is applied to confirm our theoretical claim. In addition, we control the chaotic motions to a fixed point with delay feedback method. Numerical results support the theoretical analysis.
Highlights
Extensive research has been carried out to discover complex behaviors of various discrete dynamical systems in the past several decades
Based on the Marotto theory 22, 23, we prove theoretically the existence of the LiYorke chaos in the DCML 1.1
We prove the existence of the Li-Yorke chaos in the DCML 1.1
Summary
Extensive research has been carried out to discover complex behaviors of various discrete dynamical systems in the past several decades. A rigorous verification of chaos will provide a theoretical foundation for the researchers to discover the complex behaviors in CMLs. Recently, Li et al 13, 14 theoretically analyzed the chaos in one-way coupled logistic lattice with periodic. Discrete Dynamics in Nature and Society boundary conditions and presented a chaotification method for creating spatiotemporal systems strongly chaotic. The rigorous proof of chaos has not yet been studied in diffusively coupled map lattices DCMLs with open boundary conditions, which is one important case of CMLs. Inspired by the ideas of 13, 14, 18, 19 , we have tried to answer this question. We control spatiotemporal chaotic motion in the DCML 1.1 to period-1 orbit fixed point by delay feedback and obtain the stability conditions of control.
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