Synchronization, Resonance, And Control On Neuronal Networks

The brain has about100billion neurons each of which interacts with others toconstitute complex neural networks, so that functions of memory, cognition, emotion,and behavior are generated. The dynamical behavior of neuronal networks is closelyrelated to brain functions. Neural information processing in the brain is based on thecoordinated interactions of large numbers of neurons within different brain areas.Synchronization is an important mechanism for neural information processing. But,abnormal synchronization of individual neurons plays a key role in the emergence ofsome pathological brain functions. An effective treatment for these brain diseases iscontrolling the pathological synchronization processes of the brain by externalstimulation. Moreover, noise is widespread in neuronal networks, and resonance playsan significant role in neural information transmission. Therefore, synchronization,rensonance and synchronization control on complex neuronal networks are studied inthis work.A discrete modular neuronal network of small-world subnetworks is pioneeringlyconstructed based on a map-based neuron model to investigate its synchronizationmechanisms. It is shown that all neurons realize the chaotic phase synchronization onthe bursting time scale when the coupling strength exceeds a threshold, while on thespiking time scale, they behave asynchronously. Furthermore, phase synchronizationon small-world neuronal networks is greatly facilitated by a large random rewiringprobability. The variations of coupling strengths and the probability of random linksbetween different subnetworks can always induce synchronization transitions inmodular neuronal networks.Based on this model, the phenomena of stochastic resonance and vibrationalresonance on the modular neuronal networks are studied. It is found that there existsan optimal intensity of external stimulation (noise or high-frequency driving signal),by which the dynamical response of excitable neural systems to a subthresholdlow-frequency signal reaches the peak. The resonant effect of neural systems dependsextensively on the network structure and parameters. There exists an optimaltopological structure, such that the ability of neuronal networks for weak signaldetection and transmission achieves best. Considering that abnormal synchronization of neurons may induce somepathological conditions in the brain, such as Parkinson’s disease or epilepsy, weinvestigate effective suppression of such synchronized neural activity using anexternal periodic signal and delayed feedback control, but without changing theintrinsic activities of individual neurons. In particular, the delayed feedback controlbased on mean-field activity of the neuronal network is noninvasive, since thestimulation signal tends to zero once desynchronized state is attained, which is anadvantage for practical application in deep brain stimulation.The presented results in this work could have important implications for themechanisms of neural information transmission and processing in the brain, also thetreatment of neurological diseases induced by abnormal synchronization.