Sliding bifurcations in relay control systems: an application to natural resources management

This paper is devoted to the study of the long term dynamic behavior of exploited natural resources. The focus is on the case of protected resources, namely resources that can not be harvested when they are too scarce. The model is a controlled system composed of a nonlinear second order SISO system and an on-off feedback controller. The analysis is performed through the numerical continuation of the sliding bifurcations of the system. The results show that for suitable combinations of the parameters the system can have multiple attractors.