<p>In this paper, we consider a food chain model with singular prey-taxis. We first discuss the global existence and boundedness of the unique positive classical solution for the system in a bounded interval with Neumann boundary conditions. We then analyze the global asymptotic stability and the local stability of steady states. Finally, numerical simulation is carried out to show that the formation of steady-state pattern, spatio-temporal periodic pattern, and spike pattern may appear. We observe that the existence of positive prey-taxis of top predators may be beneficial to their own survival.</p>

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Dynamic analysis of a food chain model with singular prey-taxis

  • Zhuzhen Liao,
  • Zhi-Cheng Wang

摘要

In this paper, we consider a food chain model with singular prey-taxis. We first discuss the global existence and boundedness of the unique positive classical solution for the system in a bounded interval with Neumann boundary conditions. We then analyze the global asymptotic stability and the local stability of steady states. Finally, numerical simulation is carried out to show that the formation of steady-state pattern, spatio-temporal periodic pattern, and spike pattern may appear. We observe that the existence of positive prey-taxis of top predators may be beneficial to their own survival.