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Analysis of global properties for dynamical systems by a modified digraph cell mapping method

Author

Listed:
  • Yue, Xiaole
  • Xu, Wei
  • Zhang, Ying
  • Du, Lin

Abstract

A modified procedure is proposed in this paper to solve the limitations of digraph cell mapping method in accurately analyzing the global properties of dynamical system, such as fractal basin boundaries. Firstly a rough cell structure is applied to the generalized cell mapping (GCM) method to obtain the general global properties of dynamical systems with digraph algorithm, and then a procedure based on the composite cell coordinate system method is proposed to increase the calculation accuracy. In order to further increase the calculation speed, a simple and feasible parallel strategy is applied during the creation process of one-step transition probability matrix for the GCM method. Meanwhile, the memory consumption can be greatly reduced by storing the one-step transition probability matrix as finite separate data files. The accurate global properties of two examples, a nonlinear oscillator with fractal basin structure and the Lorenz system, are demonstrated to show the effectiveness of our proposed improvement strategy.

Suggested Citation

  • Yue, Xiaole & Xu, Wei & Zhang, Ying & Du, Lin, 2018. "Analysis of global properties for dynamical systems by a modified digraph cell mapping method," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 206-212.
    • Handle: RePEc:eee:chsofr:v:111:y:2018:i:c:p:206-212
    DOI: 10.1016/j.chaos.2018.04.025
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    Citations

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    Cited by:

    1. Ma, Shichao & Wang, Liang & Ning, Xin & Yue, Xiaole & Xu, Wei, 2019. "Probabilistic responses of three-dimensional stochastic vibro-impact systems," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 308-314.
    2. Hasin Md. Muhtasim Taqi & Humaira Nafisa Ahmed & Sumit Paul & Maryam Garshasbi & Syed Mithun Ali & Golam Kabir & Sanjoy Kumar Paul, 2020. "Strategies to Manage the Impacts of the COVID-19 Pandemic in the Supply Chain: Implications for Improving Economic and Social Sustainability," Sustainability, MDPI, vol. 12(22), pages 1-25, November.
    3. Yue, Xiaole & Lv, Ge & Zhang, Ying, 2021. "Rare and hidden attractors in a periodically forced Duffing system with absolute nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    4. Yue, Xiaole & Xu, Yong & Xu, Wei & Sun, Jian-Qiao, 2019. "Probabilistic response of dynamical systems based on the global attractor with the compatible cell mapping method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 509-519.

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