Coexistence states of a Lotka Volterra cooperative system with cross diffusion

Abstract

In this work we study the steady state cross diffusive Lotka Volterra cooperative system. We have incorporated different type of cross diffusive term at each trophic level. Using bifurcation theory, we derive sufficient conditions which ensures existence of positive solutions of the system. The analysis carried out allows us to give an affirmative answer to the question that whether cooperative species under the influence of cross diffusion can co exist or not. We have also compared the results obtained for the competitive Lotka Volterra system with our results and an ecological explanation is provided to understand the difference.

Keywords

• Bifurcation theory
• Nonlinear diffusion
• Positive solutions