Pest outbreaks control: The approach of peak-to-peak dynamics

Insect pest outbreaks in natural and exploited forests are often recursive but aperiodic. We show, by means of a continuous-time model, that the randomness of these devastating episodes is a very special kind of deterministic chaos, known as peak-to-peak dynamics, since the intensity of any outbreak can be predicted from that of the previous episode. This fact allows one to solve various control problems such as the minimization of the mean damage associated with the pest outbreaks or the regularization of their time pattern.