Abstract
In this paper, we consider the dynamics of the shadow system of a kind of homogeneous diffusive predator-prey system with a strong Allee effect in prey. We mainly use the time-mapping methods to prove the existence and non-existence of the non-constant positive stationary solutions of the system in the one dimensional spatial domain. The problem is assumed to be subject to homogeneous Neumann boundary conditions.MSC:35K57, 35B09.
Highlights
In this paper, we are mainly concerned with the following homogeneous diffusive predator-prey system with a strong Allee effect in prey: ⎧ ⎪⎪⎪⎪⎪⎨ ∂u ∂t ∂v ∂t d uxx = u( u)( u b d vxx –dv
1 Introduction In this paper, we are mainly concerned with the following homogeneous diffusive predator-prey system with a strong Allee effect in prey:
4 Conclusions In this paper, we studied the existence and non-existence of the positive non-constant stationary solutions of a shadow system corresponding to a kind of diffusive homogeneous predator-prey system with Holling type-II functional response and strong Allee effect in prey
Summary
We are mainly concerned with the following homogeneous diffusive predator-prey system with a strong Allee effect in prey:. ). In [ ], the authors considered the non-existence of non-constant positive steady state solutions, and bifurcations of spatially homogeneous and non-homogeneous periodic solutions as well as non-constant steady state solutions are studied. These results allow for the phenomenon that the rich impact of the Allee effect essentially increases the system spatiotemporal complexity. ) has been considered in [ ] for finite diffusion coefficients, no results have been reported to consider the existence and non-existence of the positive non-constant steady state solutions for the shadow system corresponding to the system The purpose of this paper is to consider the existence and non-existence of positive non-constant solutions of the following elliptic equations:.
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