Shaker Rasheed, John Billingham

A Reaction-Diffusion Model For Competing Between Two Species

• Broschiertes Buch

Produktbeschreibung

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 typecan be found when the reaction-diffusion system satisfy the symmetry property and lambda = 1.

Produktdetails

• Verlag: LAP Lambert Academic Publishing
• Seitenzahl: 180
• Erscheinungstermin: 12. Juni 2017
• Englisch
• Abmessung: 220mm x 150mm x 11mm
• Gewicht: 286g
• ISBN-13: 9783330324602
• ISBN-10: 3330324600
• Artikelnr.: 48676880

Autorenporträt

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.