GLOBAL STABILITY, BIFURCATIONS AND CHAOS CONTROL IN A DISCRETE AMENSALISM MODEL WITH COVER AND SATURATION EFFECT

In this paper, we propose a discrete amensalism model incorporating cover and saturation effect. The discrete model is derived from its continuous counterpart using the piecewise constant parameter method. First, we determine the equilibria, outline the conditions for their existence, and analyze their local stability properties. Subsequently, by employing discrete equation deflation and iteration methods, we establish a set of sufficient conditions that ensure the global attractivity of the system. Our analysis demonstrates that the size of the cover and the natural growth rate of the second population significantly influence the global attractivity of the system. Next, we investigate the existence of both flip bifurcation and transcritical bifurcation near the positive and boundary equilibria under certain conditions, utilizing the central manifold theorem and bifurcation theory. To control chaos arising from flip bifurcation, we implement feedback control strategies, specifically the hybrid control method. Finally, numerical simulations verify the feasibility of our theoretical results. Our research reveals that both the presence of cover and saturation effect enhance the density of the first population, while an increase in the amensalism coefficient $ c_1 $ ultimately leads to the extinction of the first population.