Impact of the depth of the wells and multifractal analysis on stochastic resonance in a triple-well system

We analyze the stochastic resonance in a symmetric triple-well system with the depths of the wells being different. The system is subjected to a weak periodic force and Gaussian white noise with strength D. We show that the optimum value of noise intensity (D-MAX) is minimum, while the signal-to-noise ratio is maximum when the ratio (R) of the depths of the middle and side wells is 1. At D-MAX, the particle enters the middle well twice during every period of the external periodic force. When the depths of the three wells are equal (R = 1), the mean residence time (T-MR) in each well is T/4, where T is the period of the driving force. T-MR varies with parameter R; however, periodicity in switching is observed at D-MAX for any value of R. The generalized dimensions D-q decrease with an increase in noise intensity D, reach a minimum at D = D-MAX and then increase for all values of R. The alpha-f (alpha) spectrum is always of incomplete concave shape with f (alpha(min)) = 0, while f (alpha(max)) not equal 0 at any value of D and, moreover, the maximum value of alpha is minimum at D = D-MAX.