Research On Signal Transmission And Detection In Complex Networks

Since the proposal of small-world network and scale-free network, the com-plex network has become a topic of great interest in various fields. Of these, the signal transmission and the signal detection in realistic system are the most in-teresting research field. Thus, in this thesis, we study the signal transmission in complex network, investigate the signal detection in neural system, and discuss the phase synchronization both in neural system and discrete system. The thesis is organized as follows.The first chapter is an introduction. In this section, the research background, literature review, and our works are sum-marized.The second chapter introduces the basic concepts and the models of complex network, provides some typical dynamical equations and presents two models of interaction. The complex network synchronization is also discussed.In the third chapter, we present a network model of coupled oscillators to study how a weak signal is transmitted in complex networks. Through both the-oretical analysis and numerical simulations, we find that the response of other nodes to the weak signal decays exponentially with their topological distance to the signal source and the coupling strength between two neighboring nodes can be figured out by the responses. This finding can be conveniently used to detect the topology of unknown network, such as the degree distribution, clustering coefficient and community structure, etc., by choosing many fewer nodes as the signal source. Thus our approach to detect the topology of unknown network may be efficient in practical situations with large network size.In the fourth chapter, we consider the fact that signal transmission time de-lays between synaptically coupled neurons in the brain are different, and study the effects of distributed time delays on phase synchronization of bursting neu- rons. Applying the inhibitory coupled bursting Hindmarsh-Rose neurons, we find that distributed time delays in chemical coupling can induce a variety of phase-coherent dynamic behaviors. The critical mean time delay for the emer-gence of coherent behaviors is inversely proportional to both the coupling strength and the average degree. This phenomenon is robust to nonidentical external in-puts and is independent of network topology. Finally a physical theory is formu-lated to explain the emergence of coherent neuronal activity.In the fifth chapter, we study the excitations in globally coupled excitable neurons under subthreshold periodic signal, where signal phases are in disor-der. Differing from the identical phase, we find that the disordered phases may play an active part in neuron excitations. And the excitations show a best coher-ence at an optimal level of disorder. Besides, the coherence of excitation exhibit a resonance-like dependence on the coupling coefficient. Finally, an explanation is used to analyze the mechanism of excitation. Our findings may be served as an alternative explanation to understand the robust signal detection in neuron systems.In the sixth chapter, we study the self-organization of phase synchronization in coupled map scale-free networks with chaotic logistic map at each node and find that a variety of ordered spatiotemporal patterns emerge spontaneously in a regime of coupling strength. These ordered behaviors will change with the in-crease of the average links and are robust to both the system size and param-eter mismatch. A heuristic theory is given to explain the mechanism of self-organization and to figure out the regime of coupling for the ordered spatiotem-poral patterns.The seventh chapter summarizes the thesis and gives an outlook of the future study.