Dynamical complexity and stochastic resonance in a bistable system with time delay

This paper addresses the problem of stochastic resonance (SR) in a time-delayed bistable system subjected to Gaussian white noise. Differing from the conventional studies, the statistical complexity measure and the normalized Shannon entropy have been defined and employed to quantify SR phenomenon of the time-delayed bistable system. According to the definitions of statistical complexity measure and normalized Shannon entropy, a minimum of entropy illustrates that the motion of system reaches some degree of order and a maximum of statistical complexity measure implies that the system's intricate pattern tends to complexity. It has been found that for an optimal level of noise intensity, the statistical complexity measure displays a maximum and the normalized Shannon entropy exhibits a minimum, which demonstrates not only the occurrence of SR but also the severity of dynamical complexity. And the effects of different parameters on SR are also studied by means of the statistical complexity measure. To test the validity, the signal-to-noise ratio (SNR) is also calculated and a good agreement has been found between the statistical complexity measure and the SNR, which indicates that the statistical complexity measure is an effective method for quantify SR of the time-delayed bistable system.