Sliding modes in the management of renewable resources

The presence of tipping points in ecological systems implies abrupt changes in the dynamics of the ecosystem. In these piecewise-smooth dynamical systems sliding dynamics, i.e., dynamics on the switching boundary, have been reported for population models. However, the question whether or not, and if so under which conditions, sliding dynamics may occur in an optimally controlled system have not yet been studied. We explore this issue in a simple harvesting model with two regimes, and find that optimal sliding may occur if regular steady states do not exist. Hence, sliding dynamics may be part of an optimal policy.