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

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  • Du Mingjing
  • Yulan Wang

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.

Suggested Citation

  • Du Mingjing & Yulan Wang, 2019. "Some Novel Complex Dynamic Behaviors of a Class of Four-Dimensional Chaotic or Hyperchaotic Systems Based on a Meshless Collocation Method," Complexity, Hindawi, vol. 2019, pages 1-15, October.
    • Handle: RePEc:hin:complx:5034025
    DOI: 10.1155/2019/5034025
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    References listed on IDEAS

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    1. Wu, Wenjuan & Chen, Zengqiang & Yuan, Zhuzhi, 2009. "The evolution of a novel four-dimensional autonomous system: Among 3-torus, limit cycle, 2-torus, chaos and hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2340-2356.
    2. Singh, Jay Prakash & Roy, B.K., 2016. "The nature of Lyapunov exponents is (+, +, −, −). Is it a hyperchaotic system?," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 73-85.
    3. Xiaofei Zhou & Junmei Li & Yulan Wang & Wei Zhang, 2019. "Numerical Simulation of a Class of Hyperchaotic System Using Barycentric Lagrange Interpolation Collocation Method," Complexity, Hindawi, vol. 2019, pages 1-13, February.
    4. Mingjing Du & Junmei Li & Yulan Wang & Wei Zhang, 2019. "Numerical Simulation of a Class of Three-Dimensional Kolmogorov Model with Chaotic Dynamic Behavior by Using Barycentric Interpolation Collocation Method," Complexity, Hindawi, vol. 2019, pages 1-14, April.
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