ADVANCES IN A THEORY OF IMPULSIVE DIFFERENTIAL EQUATIONS AT IMPULSE-DEPENDENT TIMES, WITH APPLICATIONS TO BIO-ECONOMICS

In this article we study bio-economics of renewable resources which define processes with impulsive dynamical behavior. The biomass is modelled by an ordinary differential equation, but in a sequence of punctual times the biomass jumps by harvest. We consider that the catches are dependent of an effort parameter, the size of the biomass and the time. We suppose that the waiting time for the next harvest instant is a function of the amount captured. We establish the introductory elements for a theory of this new type of impulsive differential equations. It is shown in an example that under logistic growth and impulsive harvest it is always possible to fix a function of the length of closed seasons that determines a sustainable regulation.