Abstract

A control strategy for a class of biological population model simulating prey-predator relationship using backstepping scheme is presented, the increasing rate of predator population has the effect of reducing the growth rate of the preys, and this reduction depends on the number of encounters between individuals of the two species. The Lotka Volterra model controller is systematically designed via a recursive procedure that skillfully interlaces the choice of a Lyapunov function with the control to eliminate the undesirable chaotic oscillation. Theoretically, it has been proved that the error signal can exponentially converge to zero. Numerical simulations are presented to show the effectiveness and feasibility of the method of control. The simulations revealed that by choosing the proper parameters of the controller, there will be a stabilize chaotic dynamics of the system to the stable equilibrium point thereby making the output signal to track all kinds of reference signals.