A complete analysis of the global dynamics of a diffusive predator and toxic prey model

Yun-fei Lv, Tongtong Li, Yongzhen Pei and Rong Yuan

Applied Mathematics and Computation, 2016, vol. 291, issue C, 182-196

Abstract: Considering many species can release toxic substances to protect themselves against predators, a diffusive predator and toxic prey system with spatial heterogeneity in predator and prey populations has been investigated. For this system, we give a complete and rigorous analysis of the global dynamics with the boundedness, globally asymptotical stability, transcritical bifurcation, Hopf bifurcation and its direction, and the stability of the bifurcating periodic solutions. Meanwhile, we consider the effects of toxins produced by the prey on the dynamic behavior. The consequence of the global stability of the coexistence equilibrium is that the toxin’s intrinsic characteristic will not change the stability of the system irreversibly. Our results show that the toxin-produced by the prey (phytoplankton) may be used as a bio-control agent for the Harmful Algal Bloom problems.

Keywords: Toxin produced by phytoplankton; Diffusion; Global stability; Hopf-bifurcation; Harmful Algal Bloom (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:291:y:2016:i:c:p:182-196

DOI: 10.1016/j.amc.2016.06.040

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