The Effect Of Noise On The Dynamics Of Complex Network

As we known, there are so much kinds of noise, which our living environment isfull of. Usually, noise is no benefit for us, it’s useless. So what is the real role of noise innature? In this paper, we studied the impact of noise on the dynamical behavior in somenonlinear dynamic systems, and got the following significant rules and conclusions.In the fist chapter，the development of chaos research are summarized. Moreover,several typical network topology structure in complex network and progress ofresearching neuron dynamics are simply recommended.In the second chapter, the Hodgkin-Huxley(HH) neuron model is formulated tohelp us.After the study we demonstrate that phase noise originated from time-varyingsignal phase can enable an excitable neuron to excite spikes upon a signal even thoughthe signal amplitude is subthreshold. In addition, we find that there exists an optimalvalue on the phase noise at which the neuron’s response to the subthreshold signal canbe significantly improved, resulting in a resonance-like behavior. A phase noise can beobserved in some real situations, our study may provide a possible mechanism forunderstanding the good performances of many sensory neurons in weak signaldetection.In the third chapter, by using a neuron-like map model to denote the genericdynamics of excitable systems, Gaussian-noise-induced pattern formation in thetwo-dimensional coupled map lattices with nearest-neighbor coupling and shortcut linkshas been studied. Given the appropriate initial values and parameter regions, with allnodes concerned, some functions are introduced to analyze the evolution of patternformation. It is found that there exists a critical cbeyond which the stable rotatingspiral wave will appear. After introducing the Gaussian noise for the homogeneous region, different spatiotemporal stable patterns will be achieved. Additionally, the effectof small-world coupling strength C is discussed, there exist a reasonable scale of coupling strength can facilitate the rapid transmission of information showing the SWeffect originate from the effective shortening of typical path lengths between arbitraryspatial unite of the system.In the fourth chapter, firstly the propagation of the noise in one-dimensionalcoupled map lattice systems was discussed. Found that noise intensity enlarge graduallyduring the process of propagation, caused synchronous destruction and the avalanchephenomena in the system. We further investigate the produce process of avalanche indifferent network topology, such as the global coupling network, small-world networksand scale-free coupling network. Effect on the avalanche from interferencesignal(i.e.noise) strength and the strength of coupling between two grid points andsystem size was also analyzed.