Existence of non-constant positive stationary solutions of the shadow predator-prey systems with Allee effect

• Published in: Advances in difference equations Vol. 2014; no. 1; pp. 1 - 7
• Main Authors: Bao, Zhenhua, Liu, He
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 15.08.2014; Springer Nature B.V; BioMed Central Ltd
• Subjects: Analysis; Boundary conditions; Difference and Functional Equations; Difference equations; Diffusion; Diffusion effects; Dynamical systems; Dynamics; Functional Analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; Shadows; homogeneous diffusive predator-prey system; strong Allee effect in prey; non-constant positive stationary solutions; shadow system
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/1687-1847-2014-226

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.