Both noise and time delay play important roles in regulating the dynamical behavior in complex systems, such as chemical oscillator, nonlinear circuits, nerve system and networks. It is ever thought that noise can cau...
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Both noise and time delay play important roles in regulating the dynamical behavior in complex systems, such as chemical oscillator, nonlinear circuits, nerve system and networks. It is ever thought that noise can cause breakdown or irregularity of the nonlinear dynamical systems, for example, the thermal noise in circuit could decrease the quality of signals. Indeed, noise often plays a positive role in excitable media; it is found that the regularity can be enhanced under intermediate noise intensi- ty. One distinct example is supported as coherence resonance or stochastic resonance that appropriate noise intensity can en- hance the temporal order, regularity, signal-to-noise ratio (SNR), and even spatial regularity in network. In theoretical studies, Gaussian white noise, Gaussian colored noise, L(vy noise, and phase noise are often considered in additive or multiplicative type. For biological neurons, channel noise is often considered for transition of electric activities. In the field of pattern selec- tion and control, it is found that noise often cause breakup of target wave and spiral wave, while appropriate noise intensity is important to support the emergence of spiral wave that keeps the network under distinct spatial regularity like a pacemaker.
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