Journal Title
Title of Journal: J Dyn Diff Equat
|
Abbravation: Journal of Dynamics and Differential Equations
|
|
|
|
|
|
|
|
Authors: Tian Xie Xianshan Yang Xiong Li Hao Wang
Publish Date: 2016/09/12
Volume: 30, Issue: 2, Pages: 447-472
Abstract
Loladze et al Bull Math Biol 621137–1162 2000 proposed a highly cited stoichiometric predator–prey system which is nonsmooth and thus it is extremely difficult to analyze its global dynamics The main challenge comes from the phase plane fragmentation and parameter space partitioning in order to perform a detailed and complete global stability and bifurcation analysis Li et al J Math Biol 63901–932 2011 firstly discussed its global dynamical behavior with Holling type I functional response and found that the system has no limit cycles and the internal equilibrium is globally asymptotically stable if it exists Secondly for the system with Holling type II functional response Li et al 2011 fixed all parameters with realistic values except K to perform the bifurcation analysis and obtained some interesting phenomena for instance the appearance of bistability and many bifurcation types The aim of this paper is to provide a complete global analysis for the system with Holling type II functional response without fixing any parameter Our analysis shows that the model has far richer dynamics than those found in the previous paper Li et al 2011 for example four types of bistability appear besides the bistability between an internal equilibrium and a limit cycle as shown in Li et al 2011 the other three bistabilities occur between an internal equilibrium and a boundary equilibrium between two internal equilibria or between a boundary equilibrium and a limit cycle In addition this paper rigorously provides all possible bifurcation passways of this stoichiometric model with Holling type II functional response
Keywords:
.
|
Other Papers In This Journal:
|