The Effect of Two-Species Competition on a Lotka-Volterra Fishery Model in the Presence of Toxicity

Abstract

Competition is a crucial ecological interaction between organisms. Despite the belief that competition benefits more vigorous species since lesser species tend to die out owing to lack of resources, there are times when even stronger species populations collapse. In this research, two species of the fish population that are subject to compete for the same resources are presented and discussed. This research focuses on analyzing the influence of the competition coefficient between these two species that are exposed to toxic substances. To accomplish this, first and foremost, the competition coefficient is chosen as a bifurcation parameter. Then, several bifurcation graphs, phase planes, and time series are presented using mathematical computing software such as Maple, Matlab and XPPAUT. This research indicates that different competition coefficient rates can affect the dynamic behavior of both species. By using one-parameter bifurcation analysis, it is analyzed that there is an existence of a transcritical bifurcation point. Findings revealed that when the competition parameter passes the transcritical bifurcation point, the stability of the two species shifted from unstable saddle to asymptotically stable steady state.