Vibrational Resonance And Spatial Coherence Resonance Of Coupled Cells

During the past two decades, complex networks as an important interdisciplinary science, which has a wide range of applications in many fields, such as mathematics, physics, biology, ecology and so on. We can see the overall picture of the problem when networks of point of view was used. Networks were composed by all kinds of components, For example, in the field of biological there are neural networks, protein networks, calcium oscillations networks and metabolic networks; in the field of social scientists there are scientists cooperation networks, actors networks, student relationship networks; in the technical field there are electric power networks, transportation networks, communication networks, etc.The complexity of complex systems can be treated as two parts: one is the complexity of the components, for example, the component is described by nonlinear dynamic equations. The other one is the complexity of interactions. Noise is inevitably present in the real networks. It is because of the these complex factor that the whole system exhibits fruitful dynamic behaviors.This paper is divided into three parts. First, Response characteristics of FitzHugh-Nagumo neurons to low frequency signal have been investigated by numerical simulation. The neurons are arranged on a square-lattice and are subjected to two frequency signals. The results showed that, vibrational resonance of the membrane potential can be induced by varying the amplitude of the high frequency signal, when the control parameter is selected in the excitable region. In addition, the responses of the neurons to higher harmonic of low frequency signal have been studied, and nonlinear vibrational resonances were also found. With the increase frequency of the low frequency signal, the response of the system to low frequency signal can resonate. Thus, the double resonance can occur by changing the low frequency signal’s frequency and the high frequency signal’s amplitude. Moreover, the effects of electrical synapses and chemical synapses on vibrational resonance and nonlinear vibrational resonance of the neurons have also been studied. Effect of the number of neurons, which are subjected to two frequency signals in the square-lattice, on the response characteristic of the system was also studied. It is found that the response characteristic of electrical coupling neurons was quite different from that of chemical coupling neurons. Second, the effects of internal noise in a square-lattice H?fer calcium oscillation system have been studied numerically in the context of chemical Langevin equations. It was found that spatial pattern can be induced by internal noise and, interestingly, an optimal internal noise strength(or optimal cell size) exists which maximizes the spatial coherence of pattern, indicating the occurrence of spatial coherence resonance. The effects of control parameter and coupling strength on system’s spatial coherence have also been investigated. We found that larger internal noise strength is needed to induce spatial pattern for a small control parameter or a stronger coupling strength, and spatial coherence can be enhanced by coupling. Third, the cooperative effects of inherent stochasticity and random long-range connections(RLRCs) on synchronization and coherence resonance(CR) in networks of calcium oscillators have been investigated. Meanwhile, the temporal coherence of the calcium spike train was characterized by the reciprocal coefficient of variance(RCV). Synchronization induced by RLRCs was observed. Moreover, it was found that the RCV shows a clear peak when both inherent stochasticity and RLRCs are optimal, indicating the existence of double CR.