Abstract
The aim of this article is to study the qualitative behavior of a host-parasitoid system with a Beverton-Holt growth function for a host population and Hassell-Varley framework. Furthermore, the existence and uniqueness of a positive fixed point, permanence of solutions, local asymptotic stability of a positive fixed point and its global stability are investigated. On the other hand, it is demonstrated that the model endures Hopf bifurcation about its positive steady-state when the growth rate of the consumer is selected as a bifurcation parameter. Bifurcating and chaotic behaviors are controlled through the implementation of chaos control strategies. In the end, all mathematical discussion, especially Hopf bifurcation, methods related to the control of chaos and global asymptotic stability for a positive steady-state, is supported with suitable numerical simulations.
Highlights
The host–parasitoid interaction is the most underlying and substantial procedure in population dynamics
This paper is concerned with the investigation of some qualitative aspects of a host–parasitoid model
The model is a modification of a generalized Hassell–Varley model of a host–parasitoid system, which can be useful for the description of ecosystems
Summary
The host–parasitoid interaction is the most underlying and substantial procedure in population dynamics. Din [8] modified the host–parasitoid interaction with implementation of constant refuge effects and reported global dynamics for the proposed model. In [9], the authors modified the host–parasitoid interaction with a Pennycuick growth function for the host population and studied Neimark-Sacker bifurcation and chaos control. Liu et al [18] explored a complex behavior and bifurcation analysis for a class of host–parasitoid interaction with an application of the Allee effect and Holling type III functional response. Keeping in view the single species density-dependent model for the host population, the Ricker model [26] is a classic discrete population model, which gives the expected number Hn+1 of individuals in generation n + 1 as a function of the number of individuals in the previous generation This model is given as follows: Hn. Theoretical findings are validated through experimental and field data based on statistical analysis of previous literatures
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