STABILIZATION OF PERIOD-DOUBLING BIFURCATIONS AND IMPLICATIONS FOR CONTROL OF CHAOS

The stabilization of period doubling bifurcations for discrete-time no nlinear systems is investigated. It is shown that generically such bif urcations can be stabilized using smooth feedback, even if the lineari zed system is uncontrollable at criticality. In the course of the anal ysis, expressions are derived for bifurcation stability coefficients o f general n-dimensional systems undergoing period doubling bifurcation . A connection is determined between control of the amplitude of a per iod doubled orbit and the elimination of a period doubling cascade to chaos. For illustration, the results are applied to the Henon attracto r.