Directional Control of Bifurcation into Targeted Trajectory

Abstract

The field of bifurcation control includes several classes of problems that are actively studied with various motivations and from different points of view. The different statements of the problem are articulated by defining various objectives of applying control to the system, depending on the motivation and the specific problem. In this paper, we propose the objective of bifurcation control that is based on one of the main features of bifurcation phenomena: bifurcation generates possibilities for different scenarios to occur. We show how to find the right directions to control the system in order to ensure the realization of a favorable scenario. Our method is based on a bifurcation theorem for an abstract problem with constraints (inequalities). This theorem is further applied to controlled dynamical systems and two reasonably simple bifurcation control problems are analyzed in order to illustrate our objective and method.