Numerical sliding bifurcation analysis: an application to a relay control system

This paper is devoted to the study of the long-term dynamic behavior of exploited renewable 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 single-input-single-output system and an on-off feedback controller. Thus, the model belongs to the class of discontinuous piecewise-smooth autonomous systems for which bifurcation theory has been recently extended. The analysis is performed through the numerical continuation of the sliding bifurcations of the system, for which specialized software has been developed. The results show that for suitable combinations of the parameters the system can have multiple attractors.