Lotka--Volterra Competition Model on Graphs
Antonín Slavík
Abstract
We consider a model of two competing species of Lotka--Volterra type with diffusion (migration), where the spatial domain is an arbitrary finite graph (network). Depending on the parameters of the model, we describe the spatially homogeneous stationary states and their stability, discuss the existence and number of spatially heterogeneous stationary states, and study the asymptotic behavior of solutions.
Topics & Concepts
HomogeneousMathematicsGraphVolterra equationsDomain (mathematical analysis)Competition modelStability (learning theory)Applied mathematicsStatistical physicsComputer scienceMathematical analysisCombinatoricsNonlinear systemPhysicsProfit (economics)EconomicsMicroeconomicsMachine learningQuantum mechanicsMathematical and Theoretical Epidemiology and Ecology ModelsEvolution and Genetic DynamicsEvolutionary Game Theory and Cooperation