Global stabilization of the planar Ricker system with noisy PBC

Abstract

We apply Prediction-Based control (PBC) in order to stabilize globally a positive equilibrium of a planar Ricker's equation. We construct a closed invariant set in a strictly positive domain for the controlled map and derive conditions on control parameters ensuring that the increments of a specially constructed Lyapunov function are nonpositive on this set. By stochastic perturbation of the parameters we decrease the average values of controls providing global, as well as local, stabilization. Computer simulations illustrate our results.