[Zurück]

D. Grass, A. Crepin:
"Bifurcations of an Optimally Controlled Slow Fast Dynamics: Fishery in a Coral Reef System";
Vortrag: 11th Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics, Amsterdam; 31.05.2010 - 02.06.2010.

Coral reefs dynamics can be modeled as an interplay between fast (algae and fish) and slow (coral) variables. As a consequence, system behavior may be sensitive to initial stock sizes and the system could flip between coral-dominated and algae-dominated states. This behavior is well known from optimal control literature to sometimes result in the existence of multiple optimal solutions (Skiba points/manifold). These properties are studied here in the context of fisheries management. In particular we analyze occurring bifurcations of the optimal system with respect to the different time scales of the slow and fast dynamics. Singular perturbation theory is used to present a dynamic system description and a careful bifurcation analysis provides important insights on the intimate interplay between algae, fish and coral.