A Reaction-Diffusion Model For Competing Between Two Species

ISBN-13: 9783330324602 / Angielski / Miękka / 2017 / 180 str.

Shaker Rasheed; John Billingham

Opis

This study deals with a two component reaction-diffusion system (RDS) for competing and cooperating species. We have analyse in detail the stability and bifurcation structure of equilibrium solutions of this system, a natural extension of the Lotka-Volterra system. We find seven topologically different regions separated by bifurcation boundaries depending on the number and stability of equilibrium solutions, with four regions in which the solutions are similar to those in the Lotka-Volterra system. We study RDS in the small parameter of the range 0 lambda 1 (fast diffusion and slow reaction), and in few cases we assume lambda = O(1). We consider three types of initial conditions, and we find three types of travelling wave solutions using numerical and asymptotic methods. However, neither numerical nor asymptotic methods were able to find a particular travelling wave solution which connects a coexistence state say, (u0,w0) to an extinction state (0, 0) when 0 lambda 1. This type can be found when the reaction-diffusion system satisfy the symmetry property and lambda = 1.

O autorze

Shaker M. Rasheed, Assist. professor in Mathematics (Numerical Analysis), PhD. in Mathematics 2013, University of Nottingham, United Kingdom. Head of Department of Mathematics, Faculty of Science, University of Zakho, Kurdistan region, Iraq. Supervised 4 MSc. students and participated in program organised by Erasmus and DAAD.