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

Advances in Difference Equations

Nallappan Gunasekaran¹  Bundit Unyong²  R. Vadivel²  Grienggrai Rajchakit³  S. Vinoth⁴  K. Sathiyanathan⁴  R. Sivasamy⁵ 

[1] Department of Mathematical Sciences, Shibaura Institute of Technology, 337-8570, Saitama, Japan;Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, 83000, Phuket, Thailand;Department of Mathematics, Faculty of Science, Maejo University, 50290, Sansai, Thailand;Department of Mathematics, SRMV College of Arts and Science, Coimbatore, Tamilnadu, India;Department of Science and Humanities, M. Kumarasamy College of Engineering, Karur, Tamilnadu, India;

关键词: Leslie–Gower predator–prey model;    Ratio-dependent functional response;    Fear effect;    Allee effect;    Local stability;    Hopf bifurcation;   

DOI  :  10.1186/s13662-021-03490-x

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY