Abstract
AbstractIn the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference64 articles.
1. Chiu, K.-S., Li, T.: Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments. Math. Nachr. 292(10), 2153–2164 (2019)
2. Li, T., Pintus, N., Viglialoro, G.: Properties of solutions to porous medium problems with different sources and boundary conditions. Z. Angew. Math. Phys. 70(3), 1–18 (2019)
3. Frassu, S., Viglialoro, G.: Boundedness for a fully parabolic Keller–Segel model with sublinear segregation and superlinear aggregation. Acta Appl. Math. 171(19), 1–20 (2021)
4. Liu, B., Zhang, Y., Chen, L.: The dynamical behaviors of a Lotka–Volterra predator–prey model concerning integrated pest management. Nonlinear Anal., Real World Appl. 6(2), 227–243 (2005)
5. Wang, Q., Dai, B., Chen, Y.: Multiple periodic solutions of an impulsive predator–prey model with Holling-type IV functional response. Math. Comput. Model. 49(9–10), 1829–1836 (2009)
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