Dynamics of an impulsive predator–prey logistic population model with state-dependent

Qizhen Xiao and Binxiang Dai

Applied Mathematics and Computation, 2015, vol. 259, issue C, 220-230

Abstract: In this paper, the dynamics for a class of state-dependent impulsive predator–prey models with the logistic growth for the predator and prey species are analyzed. By a direct calculation, the existence of a semi-trivial periodic solution is obtained. Based on the geometrical analysis and biological background, the strict threshold value conditions for the existence of positive periodic solutions are depicted. The stabilities of the semi-trivial periodic solution and positive order-1 periodic solutions are proved due to the analogue of Poincaré criterion. Numerical results are carried out to illustrate the feasibility of our main results.

Keywords: Predator–prey model; Logistic growth; State-dependent; Periodic solution (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:259:y:2015:i:c:p:220-230

DOI: 10.1016/j.amc.2015.02.061

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