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Title: Stability and bifurcation analyses of a discrete Lotka–Volterra type predator–prey system with refuge effect
Authors: Yıldız
Merdan, H.
Keywords: Flip bifurcation
Lotka–Volterra type predator–prey system
Neimark–Sacker bifurcation
Refuge effect
Stability analysis
Bifurcation (mathematics)
Continuous time systems
Numerical models
System stability
Dynamical behaviors
Fixed points
Flip bifurcations
Integral steps
Lotkum–volterrum type predator–prey system
Neimark-Sacker bifurcation
Predator - Prey system
Refuge effect
Stability analyze
Predator prey systems
Issue Date: 2023
Publisher: Elsevier B.V.
Abstract: In this paper, we discuss the complex dynamical behavior of a discrete Lotka–Volterra type predator–prey model including refuge effect. The model considered is obtained from a continuous-time population model by utilizing the forward Euler method. First of all, we nondimensionalize the system to continue the analysis with fewer parameters. And then, we determine the fixed points of the dimensionless system. We investigate the dynamical behavior of the system by performing the local stability analysis for each fixed point, separately. Moreover, we analytically show the existence of flip and Neimark–Sacker bifurcations at the positive fixed point by applying the normal form theory and the center manifold theorem. Bifurcation analyses are carried out by choosing the integral step size as a bifurcation parameter. In addition, we perform numerical simulations to support and extend the analytical results. All these analyses have been done for the models with and without the refuge effect to examine the effect of refuge on the dynamics. We have concluded that the refuge has significant role on the dynamical behavior of a discrete system. Furthermore, numerical simulations underline that the large integral step size causes the chaotic behavior. © 2022 Elsevier B.V.
ISSN: 0377-0427
Appears in Collections:Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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