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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Veröffentlicht in:Advances in difference equations Jg. 2021; H. 1; S. 1 - 22
Hauptverfasser: Vinoth, S., Sivasamy, R., Sathiyanathan, K., Unyong, Bundit, Rajchakit, Grienggrai, Vadivel, R., Gunasekaran, Nallappan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 16.07.2021
Springer Nature B.V
SpringerOpen
Schlagworte:
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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Abstract 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.
AbstractList Abstract 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.
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.
ArticleNumber 338
Author Vadivel, R.
Sivasamy, R.
Vinoth, S.
Unyong, Bundit
Sathiyanathan, K.
Gunasekaran, Nallappan
Rajchakit, Grienggrai
Author_xml – sequence: 1
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  surname: Vinoth
  fullname: Vinoth, S.
  organization: Department of Mathematics, SRMV College of Arts and Science
– sequence: 2
  givenname: R.
  surname: Sivasamy
  fullname: Sivasamy, R.
  organization: Department of Science and Humanities, M. Kumarasamy College of Engineering
– sequence: 3
  givenname: K.
  surname: Sathiyanathan
  fullname: Sathiyanathan, K.
  organization: Department of Mathematics, SRMV College of Arts and Science
– sequence: 4
  givenname: Bundit
  surname: Unyong
  fullname: Unyong, Bundit
  email: bundit.u@pkru.ac.th
  organization: Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University
– sequence: 5
  givenname: Grienggrai
  surname: Rajchakit
  fullname: Rajchakit, Grienggrai
  organization: Department of Mathematics, Faculty of Science, Maejo University
– sequence: 6
  givenname: R.
  surname: Vadivel
  fullname: Vadivel, R.
  organization: Department of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University
– sequence: 7
  givenname: Nallappan
  surname: Gunasekaran
  fullname: Gunasekaran, Nallappan
  organization: Department of Mathematical Sciences, Shibaura Institute of Technology
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Keywords Leslie–Gower predator–prey model
Ratio-dependent functional response
Hopf bifurcation
Fear effect
Allee effect
Local stability
Language English
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Snippet 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...
Abstract In this article, we discuss the dynamics of a Leslie–Gower ratio-dependent predator–prey model incorporating fear in the prey population. Moreover,...
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SubjectTerms 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
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Title The dynamics of a Leslie type predator–prey model with fear and Allee effect
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