Complex Behavior in a Fish Algae Consumption Model with Impulsive Control Strategy

Abstract

This paper investigates a dynamic mathematical model of fish algae consumption with an impulsive control strategy analytically. It is proved that the system has a globally asymptotically stable algae‐eradication periodic solution and is permanent by using the theory of impulsive equations and small‐amplitude perturbation techniques. Numerical results for impulsive perturbations demonstrate the rich dynamic behavior of the system. Further, we have also compared biological control with chemical control. All these results may be useful in controlling eutrophication.