Analysis of a new coupled hyperchaotic model and its topological types

In order to construct the high-dimensional discrete hyperchaotic systems systemically, this paper proposes a new coupled chaotic model. It has a wide chaotic parameter range and can relax the election of the coupling coefficient. Sufficient conditions are derived to prove the existence of Li-Yorke chaos in the proposed model. Meanwhile, the existence of hyperchaos is also demonstrated. To discern the effects of different coupling types on the chaotic dynamics more comprehensively, we further explore the dynamical behaviors with various coupling structures by using Lyapunov spectrum, bifurcation analysis, and phase portraits. We investigate the interaction relationship between coupled units and give suggestions for selecting coupling types. The results indicate that the coupled model has more complex and more stable chaotic performance when there exists a loop in its topological structure. Further, synchronization is also discussed in this work; analysis results illustrate that the proposed model cannot be suppressed to periodic points at sufficiently high coupling strengths. This paper suggests an effective method that may contribute to studying hyperchaos design and coupled chaotic systems.

Automated summary

This paper introduces a new coupled chaotic model with a wide chaotic parameter range. By exploring dynamical behaviors with various coupling structures, it is found that the coupled model exhibits more complex and stable chaotic performance when there exists a loop in its topological structure.