Dynamic Robust Bifurcation Analysis

Abstract

We propose a new concept of dynamic robust bifurcation analysis for uncertain dynamical systems. An uncertain system is described by a feedback form composed of a nonlinear dynamical system and a dynamic uncertainty that is defined by a set of differential equations. For such an uncertain system, a bifurcation point can be uncertain as well. Therefore, we formulate a dynamic robust bifurcation analysis problem of identifying the set of all potential bifurcation points. To this end, first, we study equilibrium analysis to evaluate the existence and location of equilibria. Next, we derive a condition for robust hyperbolicity of the evaluated set of potential equilibrium points. On the basis of the condition, we propose a method for identifying the set of potential bifurcation points. Finally, illustrative examples for robustness analysis of normal forms for various bifurcations are presented.