Bifurcation structure of steady-states for a cooperative model with population flux by attractive transition

TL;DR

This paper analyzes the bifurcation structure of steady-states in a cooperative population model with flux, revealing multiple bifurcation points and the asymptotic behavior of solutions as flux increases, supported by numerical simulations.

Contribution

It provides a detailed bifurcation analysis of a cooperative model with population flux and links steady-states to scalar field solutions as flux grows large.

Findings

Multiple bifurcation points on the positive solution branch.

Steady-states approach scalar field solutions as flux tends to infinity.

Numerical simulations confirm the bifurcation structure and asymptotic behavior.

Abstract

This paper studies the steady-states to a diffusive Lotka-Volterra cooperative model with population flux by attractive transition. The first result gives many bifurcation points on the branch of the positive constant solution under the weak cooperative condition. The second result shows each steady-state approaches a solution of the scalar field equation as the coefficients of the flux tend to infinity. Indeed, the numerical simulation using pde2path exhibits the global bifurcation branch of the cooperative model with large population flux is near that of the scalar field equation.