Stochastic Resonance And Dynamical Complexity In Bistable Systems Via Statistical Complexity Measure

In nature, engineering and society, noise is ubiquitous. Usually, it is regarded as a negative effect and a source of disorder and chaotic motion of systems. However, the discovery of stochastic resonance changes our mind. Namely, noise can play a constructive role in the evolution of nonlinear system. In recent years, the phenomenon of stochastic resonance has attracted a lot of attentions and gained potential applications in many science fields. It has been studied extensively both theoretically and experimentally. Meanwhile, several classic theories and techniques have been proposed. However, the detection and quantification of stochastic resonance is still a difficult and challenging task. Thus, statistical complexity measures, as new tools, are employed to character stochastic resonance and dynamical complexity of bistable systems excited by different noises in this dissertation.Firstly, the stochastic resonance of symmetric bistable system subject to Gaussian colored noise is investigated. The statistical complexity and normalized Shannon entropy are calculated by means of stochastic fourth-order Runge-Kutta algorithm and Bandt-Pompe method. Then, the influences of colored noise intensity, correlation time, amplitude and frequency of periodic signal on stochastic resonance are investigated. Meanwhile, the expression of signal-to-noise ratio(SNR) obtained from unified colored noise approximation is presented to show the effectiveness of previous results. It is turned out that the statistical complexity and normalized Shannon entropy can be used to characterize some subtle signatures of noise-induced phenomena. Additionally, the robustness of results is verified with reducing the embedding dimension and the total length of the time series.Secondly, the problems of stochastic resonance in one dimensional symmetric bistable system and two coupled bistable systems driven by Poisson white noise are investigated, respectively. For the case of one dimensional symmetric bistable system, the effects of Poisson white noise on the mean first passage time and probability density function of first passage time are calculated numerically. Then, the statistical complexity measures are adopted to study the influence of Poisson white noise on stochastic resonance in the present of cosine signal. The non-monotonous structures of statistical complexity measures reveal the occurrence of stochastic resonance. Besides, the influences of different three weak periodic signals, including rectangular, cosine and triangle signals, on stochastic resonance are also investigated. One can see that the effect of rectangular signal on stochastic resonance is most significant among these three signals. In the case of two coupled bistable systems, the statistical complexity measures of two subsystems are calculated and analyzed with strong damping coefficient. It can be seen that the evolutions of statistical complexity measures of these two subsystems have similar dynamical behavior. Also, the influences of system parameters and Poisson white noise on stochastic resonance are considered in detail. Based on our results, it can be concluded that the big mean arrival rate can promote stochastic resonance, and the stochastic resonance is first strengthened and then weakened as increasing the coupling coefficient.Thirdly, the behavior of stochastic resonance in bistable system with time delay under Gaussian white noise is considered. Differing from conventional studies, the statistical complexity and normalized Shannon entropy are addressed as new tools to analyze the proposed problem. The effects of time delay and feedback strength on mean first passage time are investigated in detail. Then, the phenomenon of stochastic resonance is investigated with the help of statistical complexity measures when a weak periodic signal is added to the given system. It is turned out that appropriate feedback strength can suppress the occurrence of stochastic resonance, and the effect of time delay on stochastic resonance is related to the value of feedback strength. These results are verified by comparing with the outcomes obtained by SNR.Finally, the dynamical complexity is investigated in an asymmetric bistable system excited by multiplicative colored and additive white noises. Due to the asymmetry of potential function, the probability distribution from time series of consecutive residence time intervals of total system and two different potential wells are calculated by virtual of Bandt-Pompe method, respectively, and the corresponding statistical complexity and normalized Shannon entropy are obtained. On the basis of these, the effects of potential asymmetry, periodic signal, multiplicative colored and additive white noises on dynamical complexity are discussed in detail. The results demonstrate that the curves’ trends of statistical complexity and normalized Shannon entropy of given system are always different from those of two potential wells when varying the values of parameters.