On the symbiotic Lotka–Volterra model with diffusion and transport effects

Abstract

In this work we analyze the existence, stability and multiplicity of coexistence states for a symbiotic Lotka-Volterra model with general diffusivities and transport effects. Global bifurcation theory, blowing up arguments for a priori bounds, singular perturbation results, singularity theory and fixed point index in cones are among the techniques used to get our results and to explain the drastic change of behavior exhibited by the dynamics of the model between the cases of weak and strong mutualism between the species. Our methodology works out to treat much more general classes of symbiotic models.