Resonant stimulation and control of nonlinear oscillators

Accurate control of hyperbolic trajectories in any dimension

“…In particular, this will allow the long-term behavior to be made time varying in a desired fashion; essentially, trajectories will approach a user-specified nonautonomous attractor. Such a method would extend more classical control strategies which, for example, attempt to have a chaotic system approach a fixed point [51][52][53][54][55], a periodic orbit [56][57][58][59][60][61], or even a chaotic regime [62] by taking advantage of the relevant entity's stable manifold.…”

Characterization of Complex Systems by Aperiodic Driving Forces

“…For a large variety of systems this solution is stable [6]. For y (t) = x (t) the energy transfer AE = fo T F (t) idt is positive for all T and the reflected energy E, = fo T F (t) O®(-F (t) y) dt is zero, which is its smallest value.…”

“…Active methods, like nonlinear resonance spectroscopy, are superior to passive methods because of three reasons: First, a measurement of parameters of a system by an active method can be done in the region of the state space of the system that is of the most physical interest, in contrast to passive methods, which have access only to those regions of the state space which are close to the attractors. Second, the model can be used to control the dynamics of complex systems [6,7]. Third, the active method is especially superior in those cases where the che experimental system is a set of identical, weakly coupled oscillators behaving incoherently.…”

Reduction of Complexity by Optimal Driving Forces

“…Since the characteristic frequencies of nonlinear oscillators usually depends on the amplitude the optimal driving force has to be aperiodic. Recently a method to calculate those optimal driving forces has been presented [6]. We apply this method in order to calculated optimal driving forces for the creation of solitons.…”