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

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 Alle...

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Vydáno v:Advances in difference equations Ročník 2021; číslo 1; s. 1 - 22
Hlavní autoři: Vinoth, S., Sivasamy, R., Sathiyanathan, K., Unyong, Bundit, Rajchakit, Grienggrai, Vadivel, R., Gunasekaran, Nallappan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 16.07.2021
Springer Nature B.V
SpringerOpen
Témata:
Allee effect
Analysis
Behavior
Bifurcation theory
Difference and Functional Equations
Dynamic stability
Equilibrium
Existence theorems
Fear
Fear effect
Functional Analysis
Hopf bifurcation
Jacobi matrix method
Jacobian matrix
Leslie–Gower predator–prey model
Local stability
Mathematical models
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Population
Predation
Predator-prey simulation
Predators
Ratio-dependent functional response
Leslie–Gower predator–prey model
Ratio-dependent functional response
Hopf bifurcation
Fear effect
Allee effect
Local stability
ISSN:1687-1847, 1687-1839, 1687-1847
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03490-x