Taming chaotic dynamics with weak periodic perturbations

The control of chaos: theory and applications

“…Periodic [59] or stochastic [60] perturbations have been seen to produce drastic changes in the dynamics of chaotic systems, leading eventually to the stabilization of some periodic behavior. These approaches, however, are in general limited by the fact that their action is not goal oriented, i.e.…”

Stabilizing periodic orbits in a chaotic semiconductor laser

“…Suppression of chaos due to weak periodic perturbations applied on an externally driven oscillator has been proposed by Braiman and Goldhirsch [17], where an AC-driven Josephson junction equation is considered. There was added a weak external sinusoidal forcing, beside the main driving.…”

“…It was found that chaotic dynamics can be achieved by many routes, as period-doubling cascades, type-I intermittency, and crisis-induced intermittency (chaos-chaos switchings). Chaos control will be numerically demonstrated in this paper using both the OGY method [9]and the inclusion of a second injection current source [17].…”

Replicate periodic windows in the parameter space of driven oscillators

“…On the other hand, the perturbation frequency is settled in an integer ratio of the original system frequency. Similar procedures have been already reported in literature [20][21][22]. So, the time evolution of this perturbed system is determined by solution of the following dimensionless equation:…”

“…For example, a weak harmonic perturbation has been used to suppress chaos in the forced Duffing oscillator [21], and a similar perturbation has been applied to control chaos in a Josephson junction oscillator [22]. Considering that in [20][21][22] the controlling of these two well-known systems were essentially accomplished for limited ranges of system parameters, a further parameter space analysis considering a weak harmonic perturbation is required.…”