Selection of a desirable chaotic phase using small feedback control

It is common for nonlinear dynamical systems to exhibit behaviors where orbits switch between distinct chaotic phases in an intermittent fashion. A feedback control strategy using small parameter perturbations is proposed to stabilize the trajectory around a desired chaotic phase. The idea is illustrated by using an intermittent chaotic time series generated by model dynamical systems in parameter regimes after critical events such as the interior crisis. Relevance to biological situations is pointed out.