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Global dynamics of a chemotaxis system with toxicity in invasive species

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  • Yuan, Xiaoyue
  • Zhang, Xuebing
  • Liu, Wenjun
  • Moussaoui, Ali
  • Auger, Pierre

Abstract

Invasive species threaten the integrity of ecosystems by altering the structure and function of natural systems. It is crucial to predict the mode of biological invasion and control intruders. In this paper, we establish a diffusion biological invasion model with toxicant-taxis and conduct research through theoretical analysis and numerical simulation methods. We investigate the local stability of the system and find that it undergoes saddle–node bifurcation and transcritical bifurcation. We further prove the boundedness and global existence of the classical solutions of the system. By constructing appropriate Lyapunov functionals, the global stability of the positive steady state is analyzed, and the decay rate of the solution is provided. In addition, to investigate the effects of toxins and competition intensity on the survival of invasive species, we demonstrate the existence conditions of steady-state solutions through numerical simulations. By comparison, it is found that invasive species can only survive in new environments if they possess at least one advantage.

Suggested Citation

  • Yuan, Xiaoyue & Zhang, Xuebing & Liu, Wenjun & Moussaoui, Ali & Auger, Pierre, 2025. "Global dynamics of a chemotaxis system with toxicity in invasive species," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 235(C), pages 16-36.
    • Handle: RePEc:eee:matcom:v:235:y:2025:i:c:p:16-36
    DOI: 10.1016/j.matcom.2025.03.009
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    References listed on IDEAS

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    1. Das, Debabrata & Kar, T.K. & Pal, Debprasad, 2023. "The impact of invasive species on some ecological services in a harvested predator–prey system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 66-90.
    2. Yang, Feng & Song, Yongli, 2022. "Stability and spatiotemporal dynamics of a diffusive predator–prey system with generalist predator and nonlocal intraspecific competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 159-168.
    3. Fergola, P. & Cerasuolo, M. & Pollio, A. & Pinto, G. & DellaGreca, M., 2007. "Allelopathy and competition between Chlorella vulgaris and Pseudokirchneriella subcapitata: Experiments and mathematical model," Ecological Modelling, Elsevier, vol. 208(2), pages 205-214.
    4. Zhang, Zidie & Wu, Daiyong & Li, Nishan, 2024. "Predator invasion in a spatially heterogeneous predator-prey model with group defense and prey-taxis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 270-282.
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