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Complex dynamics in a singularly perturbed Hastings–Powell model with the additive Allee effect

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  • Wu, Yuhang
  • Ni, Mingkang

Abstract

In this article, we investigate the complex dynamics of the Hastings–Powell model with the additive Allee effect. Due to the differences of each species at different time scales, we establish a three-time scale model to describe the rate of change of species, dividing into fast, intermediate, and slow, through the scale transformation of parameters and variables. Based on geometric singular perturbation theory and Shilnikov bifurcation theory, we show the existence of periodic orbits and Shilnikov-type chaos. In addition, with the help of numerical simulation, we find that the severity of the additive Allee effect can weaken phenomena such as oscillation and chaos.

Suggested Citation

  • Wu, Yuhang & Ni, Mingkang, 2024. "Complex dynamics in a singularly perturbed Hastings–Powell model with the additive Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003746
    DOI: 10.1016/j.chaos.2024.114822
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    1. Panday, Pijush & Samanta, Sudip & Pal, Nikhil & Chattopadhyay, Joydev, 2020. "Delay induced multiple stability switch and chaos in a predator–prey model with fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 134-158.
    2. Chowdhury, Pranali Roy & Banerjee, Malay & Petrovskii, Sergei, 2023. "Coexistence of chaotic and non-chaotic attractors in a three-species slow–fast system," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    3. Lv, Songjuan & Zhao, Min, 2008. "The dynamic complexity of a three species food chain model," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1469-1480.
    4. Pal, Pallav Jyoti & Saha, Tapan, 2015. "Qualitative analysis of a predator–prey system with double Allee effect in prey," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 36-63.
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