GLOBAL ASYMPTOTIC STABILITY OF POSITIVE STEADY STATES OF AN n-DIMENSIONAL RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH DIFFUSION
نویسندگان
چکیده
The main concern of this paper is to study the dynamics of an n-dimensional ratio-dependent predator-prey system with diffusion. We study the dissipativeness, persistence of the system and it is shown that the unique positive constant steady state is globally asymptotically stable under some assumptions.
منابع مشابه
Permanence and global asymptotic stability of a delayed predator-prey model with Hassell-Varley type functional response
Here, a predator-prey model with Hassell-Varley type functional responses is studied. Some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable Lyapunov functional. Moreover, an example is illustrated to verify the results by simulation.
متن کاملGlobal qualitative analysis of a ratio-dependent predator–prey system
Ratio-dependent predator—prey models are favored by many animal ecologists recently as more suitable ones for predator—prey interactions where predation involves searching process. However, such models are not well studied in the sense that most results are local stability related. In this paper, we consider the global behaviors of solutions of a ratio-dependent predator—prey systems. Specifica...
متن کاملRich Dynamics of Gause-type Ratio-dependent Predator-prey System
Ratio-dependent predator-prey models are increasingly favored by field ecologists as an alternative or more suitable ones for predator-prey interactions where predation involves searching process. However, such models are not well studied mathematically in the past. In our recently work, we have shown that such models exhibit much richer dynamics than the traditional ones. This is especially tr...
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 کاملQualitative Analysis of a Diffusive Food Web Consisting of a Prey and Two Predators
Abstract. This paper is concerned with the positive steady states of a diffusive Holling type II predator-prey system, in which two predators and one prey are involved. Under homogeneous Neumann boundary conditions, the local and global asymptotic stability of the spatially homogeneous positive steady state are discussed. Moreover, the large diffusion of predator is considered by proving the no...
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 2013