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Existence of homoclinic orbit of Shilnikov type and the application in Rössler system

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  • Ding, Yuting
  • Zheng, Liyuan

Abstract

In this paper, we modify the methods of Zhou et al. (2004) and Shang and Han (2005) associated with proving the existence of a homoclinic orbit of Shilnikov type. We construct the series expressions of the solution based at a saddle-focus on stable and unstable manifolds, and give the sufficient conditions of the existence of homoclinic orbit and spiral chaos. Then, we consider the Rössler system with the typical parameters under which the system exhibits chaotic behavior. Using our modified method, we verify that there exists a homoclinic orbit of Shilnikov type in the Rössler system with a group of typical parameters, and prove the existence of spiral chaos by using the Shilnikov criterion, and we carry out numerical simulations to support the analytic results.

Suggested Citation

  • Ding, Yuting & Zheng, Liyuan, 2023. "Existence of homoclinic orbit of Shilnikov type and the application in Rössler system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 770-779.
    • Handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:770-779
    DOI: 10.1016/j.matcom.2022.12.013
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    References listed on IDEAS

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    1. Sun, Mei & Tian, Lixin & Fu, Ying, 2007. "An energy resources demand–supply system and its dynamical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 168-180.
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    Cited by:

    1. Remus-Daniel Ene & Nicolina Pop, 2024. "Semi-Analytical Closed-Form Solutions for Dynamical Rössler-Type System," Mathematics, MDPI, vol. 12(9), pages 1-18, April.

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