Relationship between invariant manifold and convergence of solution in magneto-elastic beam system under time delayed feedback control

摘要

Time delayed feedback control is well known as a practical method for stabilizing unstable periodic orbits embedded in chaotic attractors. The systems under the control method are described by delay differential equations and then become infinite dimensional systems whose phase space is in function space. However, no intrin-sic discussion has been obtained for the control characteristics associated with global dynamics in function space. In this report, we numerically are going to discuss the unstable manifold originating from the unstabilizable solution with relation to the domain of attraction of target unstable periodic orbits and transient response in stabilization.