Global dynamic behavior of a predator–prey model under ratio-dependent state impulsive control.

• Use Ratio-Dependent State Impulse-Control to control a predator–prey system with square root functional response. • The controlled system exists a unique k-periodic solution by using the Brouwer's fixed point theorem. • There exist orbitally asymptotically stable order-1 and order-2 periodic solutions. This paper studies the global dynamic behavior of a prey–predator model with square root functional response under ratio-dependent state impulsive control strategy. It is shown that the boundary equilibrium point of the controlled system is globally asymptotically stable. An order-k periodic orbit is obtained by employing the Brouwer's fixed point theorem. Furthermore, the critical values are determined for the existence of orbitally asymptotically stable order-1 and order-2 periodic orbits in finite time. These critical values play an important role in determining different kinds of order-k periodic orbits and can also be used for designing the control parameters to obtain the desirable dynamic behavior of the controlled prey–predator system. Moreover, it is found that the local equilibrium point is also globally asymptotically stable under the control strategy. Numerical examples are provided to validate the effectiveness and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]