Realistic threshold policy with hysteresis to control predator–prey continuous dynamics

This paper introduces a threshold policy with hysteresis (TPH) for the control of one-predator one-prey models. The models studied are the Lotka–Volterra and Rosenzweig–MacArthur two species density-dependent predator–prey models and the Arditi–Ginzburg nondimensional ratio-dependent model. The proposed policy (TPH) changes the dynamics of the system in such a way that a bounded oscillation is achieved confined to a region that does not allow extinction of either species. The policy can be designed by a suitable choice of so called virtual equilibrium points in a simple and intuitive manner.

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