[MS10] Model Bifurcations and Ecological Relevance

[MS10-04] Transient solutions and critical times of diffusive Lotka-Volterra strong-weak competition system

*Mohd Almie Bin Alias¹, Nor Farah Wahidah Binti Nor Khalid¹ (1. Universiti Kebangsaan Malaysia (Malaysia))

Keywords:

strong-weak competition,mean action time,Fisher-KPP equation,critical time

In this study, we considered the diffusive Lotka-Volterra strong-weak competition system comprising the superior and inferior species in a bounded domain. The effect of various types of initial distributions of both species on their growth and decay was investigated. We calculated numerically the critical time, defined by the time taken for each species to approach its steady state at a predetermined threshold. While travelling wave solutions were seen in most cases, wave-splitting and pursuit-and-evasion-like phenomena were occasionally observed. Based on the correspondence between the transient solutions and the critical times, we managed to deduce how the initial distributions of species affect the critical time. We also compared the numerical critical times with the probabilistically-derived mean action times, which produced a good match. By reducing the coupled system to the single Fisher-KPP equation, we obtained the bounds on critical time for restricted type of initial species distributions.