Synchronization And Resonance Dynamics Of Complex Neural Networks Under Noise And Coupling Delay

A neuron in the cerebral cortex may connect to nearly104postsynaptic neurons via synapses, leading to the connection architecture of the cerebral cortex very complicated. Information processing in the neural systems is based on the coordinated interactions of large numbers of neurons. As is well known, noise is inevitable in neural systems. Moreover, time delays are inherent to neural systems due to the finite propagation speeds as well as time lapses occurring by both dendritic and synaptic processing. Thus it is significant to understand how noise and time delays affect the collective dynamics of complex neuronal networks. Based on the theory and technique of nonlinear dynamical systems and stochastic process, this dissertation is devoted to discussing the nontrivial influences of bounded noise, diversity represented by quenched noise, as well as time-delayed coupling on the synchronization and resonance dynamics of complex neuronal networks. The main contents and conclusions are as follows.1. The influences of bounded noise together with shortcuts on the spatiotemporal dynamics of neuronal networks are investigated. Firstly, we focus on the case of nearest-neighbor coupled neuronal networks. The numerical results show that bounded noise can impair the synchronizability among coupled neurons, while coherence resonance occurs at an intermediate level of noise amplitude. Then, we introduce shortcuts to the nearest-neighbor coupled networks to formulate small-world networks. The results indicate that the synchronization and coherence resonance in the networks can be enhanced with the addition of shortcuts. Moreover, we verify that there exists an intermediate value of the adding probability such that the small-world networks reach much more ordered spatiotemporal patterns, i.e., the coupled neurons are most coherent in time and nearly synchronized in space. In addition, the shortcuts-induced much more ordered states are confirmed to be robust against changes of the intensity of the unit Wiener process.2. A model of scale-free neuronal networks, which consists of diverse Fitzhugh-Nagumo neurons and time-delayed coupling, is firstly constructed. Then, this work has proposed to explore the nontrivial effects of diversity and time-delayed coupling on the resonance dynamics by numerical simulation in this model. When the delays in the coupling are absent, the result has shown that the response of the neuronal networks to an external subthreshold periodic signal is optimized at an intermediate level of diversity, namely, an appropriate tuned level of diversity can induce resonance in the scale-free neuronal networks. This phenomenon is also confirmed to be robust to changes of the coupling strength. In addition, we find that delays in the coupling have significant influences on the resonance dynamics. It is revealed that proper delays can induce multiple resonances in the scale-free neuronal networks, which appears at each multiple of the oscillation period of the signal. Moreover, the performance of fine tuned delays in inducing multiple resonances can be also clearly observed when diversity is within an appropriate range.3. Neuroanatomic studies have revealed that neurons with similar connectional and functional features are arranged into distinctive modules. Modules are formed by areas that are densely linked with other areas in the same module but sparsely linked with areas in other modules. On the basis of section2we further discuss the influences of diversity and time-delayed coupling on the resonance dynamics of a modular network consisting of small-world subnetworks. When the delay is vanished in the coupling, it is shown that an intermediate level of diversity can also induce resonance in the modular neuronal network. Moreover, an intermediate value of the adding probability of the small-world subnetworks warrants the emergence of the pronounced resonance phenomenon, while resonance is always impaired upon increasing the number of subnetworks. On the other hand, it is revealed that, irrespectively of the number of the subnetworks, proper delays can also induce multiple resonances in the neuronal network. In addition, the phenomenon of delay-induced multiple resonances can also be clearly observed for diversity that lies in an appropriate range.