Robust control of period doubling bifurcations and implications forcontrol of chaos

摘要

The stabilization of period doubling bifurcations fordiscrete-time nonlinear systems is investigated. Both static and dynamicfeedback controllers have been studied. It is shown that genericallysuch bifurcations can be stabilized using smooth feedback, even if thelinearized system is uncontrollable at criticality. A connection isdetermined between control of the amplitude of a period doubled orbitand the elimination of a period doubling cascade to chaos. Forillustration, the results are applied to the Henon system