The dynamics of a Leslie type predator–prey model with fear and Allee effect

Autor:	K. Sathiyanathan, Grienggrai Rajchakit, R. Vadivel, S. Vinoth, Nallappan Gunasekaran, R. Sivasamy, Bundit Unyong
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	Lyapunov function Population 01 natural sciences Leslie–Gower predator–prey model 010305 fluids & plasmas Allee effect symbols.namesake Limit cycle 0103 physical sciences QA1-939 Applied mathematics Quantitative Biology::Populations and Evolution Hopf bifurcation education 010301 acoustics Bifurcation Mathematics education.field_of_study Algebra and Number Theory Fear effect Phase portrait Applied Mathematics Ratio-dependent functional response Local stability Ordinary differential equation Jacobian matrix and determinant symbols Analysis
Zdroj:	Advances in Difference Equations, Vol 2021, Iss 1, Pp 1-22 (2021)
ISSN:	1687-1847
Popis:	In this article, we discuss the dynamics of a Leslie–Gower ratio-dependent predator–prey model incorporating fear in the prey population. Moreover, the Allee effect in the predator growth is added into account from both biological and mathematical points of view. We explore the influence of the Allee and fear effect on the existence of all positive equilibria. Furthermore, the local stability properties and possible bifurcation behaviors of the proposed system about positive equilibria are discussed with the help of trace and determinant values of the Jacobian matrix. With the help of Sotomayor’s theorem, the conditions for existence of saddle-node bifurcation are derived. Also, we show that the proposed system admits limit cycle dynamics, and its stability is discussed with the value of first Lyapunov coefficient. Moreover, the numerical simulations including phase portrait, one- and two-parameter bifurcation diagrams are performed to validate our important findings.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2131773aa08cd889b6ff995b3e5cae7b https://doaj.org/article/92eebb3e41324c6d811330174ac55abe Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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