BIFURCATION ANALYSIS FOR AROWANA FISH MODEL WITH HARVESTING EFFECT

Abstract

Wild Asian arowana fish has been an endangered species since 1976 as we need to pay attention to this species to avoid its extinction by chance. Factors that threaten the population of wild arowana fish included its own reproductive method and spawning location. This research is aimed to consider a mathematical model of wild Arowana fish with its prey to easily understand the dynamics of both populations. The model is analyzed both analytically and numerically. We solved the model to obtain equilibria and analyse the stability of equilibria by determining the eigenvalues of Jacobian Matrix of the model considered. The bifurcation analysis was also performed, in which the harvesting rate has been chosen as critical parameter. The results proves that three equilibrium points were found, and the stability condition of these equilibria was analysed. It also turns out that the model undergoes a transcritical bifurcation. Time series and phase portrait were also plotted to see the changes of dynamics for both population for different values of harvesting parameter. Thus, this research is important to educate and increase awareness among human to control their fishing behaviour so that arowana population can be sustained in the future.