Some Novel Complex Dynamic Behaviors of a Class of Four-Dimensional Chaotic or Hyperchaotic Systems Based on a Meshless Collocation Method

Du Mingjing,Yulan Wang

doi:10.1155/2019/5034025

Abstract

In the field of complex systems, there is a need for better methods of knowledge discovery due to their nonlinear dynamics. The numerical simulation of chaotic or hyperchaotic system is mainly performed by the fourth-order Runge–Kutta method, and other methods are rarely reported in previous work. A new method, which divides the entire intervals into N equal subintervals based on a meshless collocation method, has been constructed in this paper. Some new complex dynamical behaviors are shown by using this new approach, and the results are in good agreement with those obtained by the fourth-order Runge–Kutta method.

Highlights

In recent years, some new four-dimensional chaotic or hyperchaotic systems [1,2,3,4,5,6,7] are presented
In [2], the authors reported a four-dimensional dissipative chaotic system, and the coexistence of rich chaotic dynamics in the system was investigated through the Lyapunov spectrum, bifurcation diagram, Poincaremap, frequency spectrum, and attractor plot
In [4], Complexity a four-dimensional autonomous system with complex hyperchaotic dynamics was presented, and the complex dynamical behaviors were investigated by dynamical analysis approaches, such as time series, Lyapunov exponent spectra, bifurcation diagram, and phase portraits

Summary

Introduction

Some new four-dimensional chaotic or hyperchaotic systems [1,2,3,4,5,6,7] are presented. In [1], the authors presented a four-dimensional hyperchaotic system and investigated and analyzed some complex dynamical behaviors such as ultimate boundedness, chaos, and hyperchaos. In [1,2,3,4,5,6,7,8], the authors used the fourth-order Runge–Kutta method to simulate chaotic or hyperchaotic systems. We mainly introduce an improved meshless collocation method to simulate hyperchaotic systems with long-time dynamic behavior.

Results

Conclusion