Efficient strategy for the occasionally proportional feedback method in controlling chaos

In this work, the generic mechanism of the occasionally proportional feedback (OPF) technique in controlling chaos has been explored extensively. Except for stabilizing the unstable states that are embedded in the chaotic attractors, the OPF method is also found to generate a great number of new states during the control processes. The forms and characteristics of these new states have been addressed. Moreover, we clarify the roles of the parameters in the OPF method and this clarification leads to a practical and systematic approach in adjusting the parameters for control. To demonstrate the validity, an analogous electronic circuit of the resistively shunted Josephson junction oscillator is employed in addition to a numerical illustration of the logistic mapping.