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

Abstract

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.

A Complexity-Based Approach for the Detection of Weak Signals in Ocean Ambient Noise

“…However, it can be observed from spectrogram in Figure 2 that, beyond −14.4 dB, the presence of the ship signal is not recognizable in ambient noise. One study [38] has shown that SNR has good agreement with SCM. This feature enabled the SCM to describe stochastic resonance by comparing with the SNR [38].…”

“…One study [38] has shown that SNR has good agreement with SCM. This feature enabled the SCM to describe stochastic resonance by comparing with the SNR [38]. To ensure that the results presented in Figure 3 are not due to stochastic fluctuations, we computed H SCM and C SCM for the ship signal at´19.2 dB and ambient noise at every 9 s (60 s duration, segregated to form seven signals, each of duration 9 s).…”

Applying the Optimal Injected Noise to Signal Estimation via Adaptive Stochastic Resonance

“…It is a well-established fact nowadays that a suitable amount of noise can result in an improved performance of certain nonlinear systems, and such favorable use of injected noise is the so-called stochastic resonance phenomenon [1][2][3]. In recent years, the phenomenon of stochastic resonance has been the subject of considerable interest in various research fields, such as physics [4][5][6][7], biomedicine [8], signal processing [9,10] and neural networks [11][12][13]. However, a complicated question is to characterize the optimal level, or even better the optimal probability density function (PDF), of the noise to be purposefully injected in a given nonlinear process in order to maximize the performance.…”

Stochastic Resonance in a Multistable System Driven by Gaussian Noise

“…There have been many theoretical developments of SR in conventional bistable systems [7][8][9][10][11][12]. Recently, there have appeared some extensions of SR, such as stochastic resonance in a harmonic oscillator [13], ghost stochastic resonance in the FitzHugh-Nagumo neuron model [14,15], Transition in a Bistable Duffing System [16], time delay SR [17], trichotomous noise induced SR in a linear system [18], and superthreshold SR [19]. Literature [20][21][22] proposes a new model of multistable system.…”

“…Literature [20][21][22] proposes a new model of multistable system. However, [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] did not study the SNR. In this paper, we use the model of multistable system driven by periodic signal and white noise which can realize the maximum utilization of noise and obtain better detection effects.…”