Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6892317 | Computers & Mathematics with Applications | 2017 | 12 Pages |
Abstract
In this paper, we consider a reaction-diffusion system describing a three-species Lotka-Volterra food chain model with homogeneous Dirichlet boundary conditions. By regarding the birth rate of prey r1 as a bifurcation parameter, the global bifurcation of positive steady-state solutions from the semi-trivial solution set is obtained via the bifurcation theory. The results show that if the birth rate of mid-level predator and top predator are located in the regions 0λ1, respectively. Then the three species can co-exist provided the birth rate of prey exceeds a critical value. Moreover, an explicit expression of coexistence steady-state solutions is constructed by applying the implicit function theorem. It is demonstrated that the explicit coexistence steady-state solutions is locally asymptotically stable.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Zhan-Ping Ma, Yu-Xia Wang,