Global aspect of steady-states for competitive-diffusive systems with homogeneous Dirichlet conditions
A coupled pair of diffusion equations in one space variable is considered under Lotka-Volterra dynamics and homogeneous Dirichlet boundary conditions. Using primarily bifurcation theory methods and linearized stability analysis the author obtains a fairly complete (although not a totally complete) description of the existence and stability properties of nonnegative and positive stationary solutions as they depend upon the two diffusion coefficients. Of particular interest is the demonstration (analytically and numerically) of the possible existence of stable positive stationary solutions for values of the interaction coefficients which allow no positive equilibrium solutions for the nondiffusion Lotka- Volterra equations.
scientific article; zbMATH DE number 3944399
scientific article