A Competition and Harvesting Model Applied to a Fish Population Along the Moroccan Cost

Abstract

Objectives: The aims of this paper is to study the dynamics of three populations of fish living along the Moroccan Atlantic costs. Methodology: Using ordinary differential equations, a mathematical model is proposed, assuming competition between neighbouring populations and harvesting. Local Stability of equilibrium points is given and Liapunov function is used to show global stability. Results: The proposed mathematical model has 8 equilibrium points of which 3 are seen to be unstable, 4 are stable under conditions on parameters and the 8th equilibrium point with all components positive is seen to be globally stable. Conclusion: Assuming that a total constant fishing effort E is shared between the three zones, the steady states analysis shows that stability of equilibrium points P2 and P4-P6 depends on the level of the harvest aiqiE in each zone i while the equilibrium point P7 is globally asymptotically stable provided conditions of existence are satisfied, meaning that under a constant total effort (E = a1E + a2E + a3E), viability and sustainability of fish populations in the three zones is not altered by the degree of fishing effort aiE.