A characteristic frequency of chaotic dynamical system
Headline's characteristic frequency is the frequency of a periodical external force which -- having a sufficiently large amplitude -- can synchronise a chaotic motion. Author's heuristic idea is: using the concept of ``analytical signal'' and a computed (or measured) solution of a chaotic motion this characteristic frequency can be calculated easily supposing this is the most probable ``instantaneous frequency'' of the solution. Examination of this assumption is carried out on two well-known systems: the Chua and the Lorenz system. Physical mechanism of oscillation excitation is considered different of these systems and therefore hoped the result will be sufficiently general. Synchronisation regions of the Chua oscillator were found numerically; one of these regions is near to a frequency calculated with the aid of the corresponding linear system; another region is in the vicinity of the most probable instantaneous frequency calculated according to author's suppositions. The author tries to apply his assumption for a periodically driven nonlinear oscillator, the Duffing one, executing chaotic oscillations. Calculating the most probable instantaneous frequency and inserting another external force with this frequency an amplitude threshold was found above which synchronisation of the chaotic oscillations occured. The author hopes this characteristic frequency can be useful for monitoring and diagnosis of certain dynamical systems.
periodically driven nonlinear oscillator
scientific article; zbMATH DE number 558820