Diffusive induced global dynamics and bifurcation in a predator-prey system
نویسنده
چکیده
In this paper, a diffusive Leslie-type predator-prey model is investigated. The existence of a global positive solution, persistence, stability of the equilibria and Hopf bifurcation are studied respectively. By calculating the normal form on the center manifold, the formulas determining the direction and the stability of Hopf bifurcations are explicitly derived. Finally, our theoretical results are illustrated by a model with homogeneous kernels and one-dimensional spatial domain.
منابع مشابه
Hopf bifurcation analysis of a diffusive predator-prey model with Monod-Haldane response
In this paper, we have studied the diffusive predator-prey model with Monod-Haldane functional response. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. We also study the spatially homogeneous and non-homogeneous periodic solutions through all parameters of the system which are spati...
متن کاملDynamics of an eco-epidemic model with stage structure for predator
The predator-prey model with stage structure for predator is generalized in the context of ecoepidemiology, where the prey population is infected by a microparasite and the predator completely avoids consuming the infected prey. The intraspecific competition of infected prey is considered. All the equilibria are characterized and the existence of a Hopf bifurcation at the coexistence equilibriu...
متن کاملThe Dynamical Analysis of a Delayed Prey-Predator Model with a Refuge-Stage Structure Prey Population
A mathematical model describing the dynamics of a delayed stage structure prey - predator system with prey refuge is considered. The existence, uniqueness and bounded- ness of the solution are discussed. All the feasibl e equilibrium points are determined. The stability analysis of them are investigated. By employ ing the time delay as the bifurcation parame...
متن کاملThreshold harvesting policy and delayed ratio-dependent functional response predator-prey model
This paper deals with a delayed ratio-dependent functional response predator-prey model with a threshold harvesting policy. We study the equilibria of the system before and after the threshold. We show that the threshold harvesting can improve the undesirable behavior such as nonexistence of interior equilibria. The global analysis of the model as well as boundedness and permanence properties a...
متن کاملGlobal bifurcation analysis and pattern formation in homogeneous diffusive predator–prey systems
The dynamics of a general diffusive predator–prey system is considered. Existence and nonexistence of non-constant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation. Bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as non-constant steady state solutions are studied. © 2015 Elsevier Inc. All rights reser...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017