Linear feedback stabilization of bifurcations and critical nonlinear systems

The efficacy of linear feedback in the stabilization of stationary and Hopf bifurcations, and, concurrently, of critical nonlinear systems, is considered. For simplicity, this presentation focuses on the linear analytic case. Through a sign requirement on associated bifurcation coefficients, sufficient conditions are obtained for the existence of stabilizing linear feedbacks. The analysis also facilitates construction of classes of stabilizing linear feedback control laws