Ultimate boundedness conditions for a hybrid model of population dynamics

This paper addresses the ultimate boundedness and permanence analysis for a Lotka-Volterra type system with switching of parameter values. Two new approaches for the constructing of common Lyapunov function for the family of subsystems corresponding to the switched system are suggested. Sufficient conditions in terms of linear inequalities are obtained to guarantee that the solutions of the considered system are ultimately bounded or permanent for an arbitrary switching signal. An example is presented to demonstrate the effectiveness of the proposed approaches.