RESUMO
We apply an analytical signal analysis to strange nonchaotic dynamics. Through this technique it is possible to obtain the spectrum of instantaneous intrinsic mode frequencies that are present in a given signal. We find that the second-mode frequency and its variance are good order parameters for dynamical transitions from quasiperiodic tori to strange nonchaotic attractors (SNAs) and from SNAs to chaotic attractors. Phase fluctuation analysis shows that SNAs and chaotic attractors behave identically within short time windows as a consequence of local instabilities in the dynamics. In longer time windows, however, the globally stable character of SNAs becomes apparent. This methodology can be of great utility in the analysis of experimental time series, and representative applications are made to signals obtained from Rössler and Duffing oscillators.
RESUMO
We demonstrate a technique for the enhancement of chaos in a computational model of a periodically stimulated excitable neuron. "Anticontrol" of chaos is achieved through intermittent adaptive intervention, which is based on finite-time Lyapunov exponents measured from the time series. Our results suggest that an adaptive strategy for chaos anticontrol is viable for increasing the complexity in physiological systems that are typically both noisy and nonstationary.
