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<p>In this paper, the dynamics of a three dimensional ODEs system is analized. This differential system corresponds to a Leslie type intraguild predation interaction between three species (a prey population, P; a mesopredator population, MP; and a superpredator population, SP). The main premises to formulate this model are the consideration of fear effects on the prey population induced by MP and SP populations, and that the interactions are governed by general functional responses. In this regard, the main result consists in to show that, independently of the prey growth rate and the functional responses, there are parameter conditions under which the corresponding differential system has a coexistence equilibrium point and it exhibits a Zero Hopf bifurcation, with respect to the parameters <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(c_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>c</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(k_1,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> which measure the predator coefficient efficiency and the mesopredator fear effect on prey, respectively. On the other hand, on assuming that the prey population has a logistic Richards growth rate and that the functional responses are Holling type, the coexistence of the three species is showed. Finally, derived from the bifurcation results, it is numerically shown that the IGP-model has a chaotic dynamics. This is done by computing the maximum Lyapunov exponents. Moreover, several invariant sets are detected, such as equilibrium points, stable limit cycles, homoclinic orbits and invariant tori.</p>

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Chaotic Dynamics of a Leslie Type Intraguild Predation Model with Predators Fear Effects on Prey and General Functional Responses

  • 期刊论文

  • 发表日期：

    2025年1月10日

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  • Gamaliel Blé,
  • Miguel Angel Dela-Rosa,
  • Fidadelfo Mondragón-Sánchez

摘要

In this paper, the dynamics of a three dimensional ODEs system is analized. This differential system corresponds to a Leslie type intraguild predation interaction between three species (a prey population, P; a mesopredator population, MP; and a superpredator population, SP). The main premises to formulate this model are the consideration of fear effects on the prey population induced by MP and SP populations, and that the interactions are governed by general functional responses. In this regard, the main result consists in to show that, independently of the prey growth rate and the functional responses, there are parameter conditions under which the corresponding differential system has a coexistence equilibrium point and it exhibits a Zero Hopf bifurcation, with respect to the parameters \(c_1\) c 1 and \(k_1,\) k 1 , which measure the predator coefficient efficiency and the mesopredator fear effect on prey, respectively. On the other hand, on assuming that the prey population has a logistic Richards growth rate and that the functional responses are Holling type, the coexistence of the three species is showed. Finally, derived from the bifurcation results, it is numerically shown that the IGP-model has a chaotic dynamics. This is done by computing the maximum Lyapunov exponents. Moreover, several invariant sets are detected, such as equilibrium points, stable limit cycles, homoclinic orbits and invariant tori.