Abstract
In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings.
Highlights
The study of the dynamics relationship of the prey-predator system has long been and will continue to be one of the dominant subjects in both ecology and mathematical ecology due to its universal existence and importance
5 Conclusion The effect of predation in the dynamics of the prey-predator model plays an essential role in the equilibrium of the ecosystem, because it allows natural mechanisms of regulation of
We have shown the dynamic behavior of our model under different values of the predation rate
Summary
The study of the dynamics relationship of the prey-predator system has long been and will continue to be one of the dominant subjects in both ecology and mathematical ecology due to its universal existence and importance. Mathematical modeling of the population dynamics of a prey-predator system is an important objective of mathematical models in biology, which has attracted the attention of many researchers [1,2,3,4] Many authors, such as Holling 1959 [5], Getz 1984, and Arditi and Ginzburg 1989 [6, 7], studied the prey-predator system with various functional responses. These different types of functional responses present a key element for understanding the dynamics of these populations.
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