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Title: Effects of the random walk and the maturation period in a diffusive predator–prey system with two discrete delays
Authors: Bilazeroğlu, Ş.
Göktepe, S.
Merdan, H.
Keywords: Delay differential equations
Discrete time delays
Functional partial differential equations
Hopf bifurcation
Periodic solutions
Population dynamics
Reaction–diffusion system
Boundary conditions
Partial differential equations
Predator prey systems
System stability
Time delay
Delay differential equations
Diffusive predator-prey system
Discrete delay
Discrete time delay
Functional partial differential equation
Hopf bifurcation analysis
Maturation periods
Periodic solution
Random Walk
Reaction diffusion systems
Hopf bifurcation
Issue Date: 2023
Publisher: Elsevier Ltd
Abstract: This study aims to present a complete Hopf bifurcation analysis of a model describing the relationship between prey and predator. A ratio-dependent reaction–diffusion system with two discrete time delays operating under Neumann boundary conditions governs the model that represents this competition. The bifurcation parameter for the analysis is a delay parameter that reflects the amount of time needed for the predator to be able to hunt. Bilazeroğlu and Merdan's algorithm (Bilazeroğlu et al., 2021), which is developed by using the center manifold theorem and normal form theory, is used to establish the existence of Hopf bifurcations and also the stability of the bifurcating periodic solutions. The same procedure is used to illustrate some specific bifurcation properties, such as direction, stability, and period. Furthermore, by examining a model with constant coefficients, we also analyze how diffusion and the amount of time needed for prey to mature impact the model's dynamics. To support the obtained analytical results, we also run some numerical simulations. The results indicate that the dynamic of the mathematical model is significantly influenced by diffusion, the amount of time needed for the predator to gain the capacity to hunt, and the amount of time required for prey to reach maturity that the predator can hunt. © 2023 Elsevier Ltd
ISSN: 0960-0779
Appears in Collections:Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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