title: May chaos always be suppressed by parametric perturbations?
abstract: The problem of chaos suppression by parametric perturbations is considered. Despite the widespread opinion that chaotic behavior may be stabilized by perturbations of any system parameter, we construct a counterexample showing that this is not necessarily the case. In general, chaos suppression means that parametric perturbations should be applied within a set of parameters at which the system has a positive maximal Lyapunov exponent. Analyzing the known Duffing-Holmes model by a Melnikov method, we showed that chaotic dynamics cannot be suppressed by harmonic perturbations of a certain parameter, independently from the other parameter values. Thus, to stabilize the behavior of chaotic systems, the perturbation and parameters should be carefully chosen.
authors.affiliation: Department of Physics, Humboldt University, Berlin, Germany.
authors.forename: Tilo
authors.initials: T
authors.lastname: Schwalger
authors.forename: Arsen
authors.initials: A
authors.lastname: Dzhanoev
authors.forename: Alexander
authors.initials: A
authors.lastname: Loskutov