SEARCHING PERIODIC-ORBITS WITH A MODULATION BASED ON SHANNON ENTROPY

It is known that a variety of stable periodic orbits can be created if a weak periodic perturbation is applied to a deep chaotic state. Howe ver, which orbit can be created is unpredictable. Because the periodic ity of a time series can be determined by a Shannon entropy, we sugges t that these orbits can be distinguished by this entropy and we may fi nd the desired periodic orbit if we can further modify the perturbatio n guiding ourselves by this entropy. Thus, the method may provide a go al-oriented scheme for taming chaos with a weak periodic perturbation. We show theoretically the scheme in three different models, namely, a modified logistic mapping, a driven Duffing-Holmes oscillator, and a directly modulated semiconductor laser. The influence of noise is disc ussed and the efficiency of searching is estimated.