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. Academic PressKey Words: blowing up for a priori bounds in systems; local and global bifurcation theory; singularity theory; fixed point index in cones; singular perturbations.

A Trait-Based Model for Describing the Adaptive Dynamics of Coral-Algae Symbiosis

“…The simplest model for studying symbiotic relationships is described by Murray (2002) and consists of two interacting populations, similarly to the classic Lotka-Volterra predatorprey system. Symbiotic models based on the Lotka-Volterra formulation have attracted the interest of many mathematicians (Korman and Leung, 1987;Lou, 1996;Delgado et al, 2000;Pao, 2005) because they are suitable for studying existence, non-existence, uniqueness or multiplicity of solutions using various techniques (Delgado and Suárez, 2009).…”

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Existence and Uniqueness of Positive Large Solutions to Some Cooperative Elliptic Systems

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