A Method for Stability and Bifurcation Control

Abstract—In this note, we use the Rössler system as an illustrative example to present a method for controlling stability and bifurcations of nonlinear dynamical systems. This approach employs the idea used in computing the transition variety sets of constrained bifurcations to find the stability boundaries of equilibrium points in parameter space. With this method and feedback control, one can obtain appropriate parameter values to delay either static, dynamic, or both bifurcations. A feedback controller is designed to stabilize the Rössler system using all feasible control parameters. A numerical example is given to demonstrate the theoretical results. Index Terms—Bifurcation control, Rössler system, stability boundary, transition variety