Detecting and measuring stochastic resonance in fractional-order systems via statistical complexity

Fractional-order systems are utilized widely to model material or physical systems with the properties of memory, non-locality and history-dependent, thus massive studies have been drawn on their dynamics during the past decade. In this paper, we are motivated to study stochastic dynamics in a fractional-order system subjected to Gaussian noise. The statistical complexity measure (SCM), an approach of information theory, has been well defined and calculated in the fractional-order Langevin model based on its Shannon entropy, by which the stochastic resonance (SR)response has been detected and measured. To compare, we further derive the equivalent system by means of the minimum mean square error rule to estimate the signal-to-noise ratio (SNR). It has been found that the SCM and the SNR depict analogous profile and exhibit peaks almost at the same level of noise. Varying the signal frequency, the SCM even quantifies Multiple-SR that SNR does not measure in the fractional-order Langevin model. Thus, the SCM may be utilized as an alternative candidate to measure SR response in bistable fractional-order systems.