| The information processing is completed by neuronal colony in neuronal system. So the movement pattern of neuronal colony is very important for the transmission of information. A single neuron can thus not implement the temporal codes of the neuron spike trains. However, the neuronal colony can give the common synapse electric current by the synchronous mode. Synchronizations widely exist in the different biological systems. Synchronization is not always desirable. For example, synchronization of individual neurons leads to the emergence of pathological rhythmic brain activity in Parkinson's disease, essential tremor, and epilepsies. Therefore, it is important to find various methods to suppress or facilitate the synchronization of coupled neuronal systems. These can discover the methods which can effectively eliminate the Parkinson syndrome and the insane epilepsy and help people to know the entire function of human brain. Recently, the research of synchronization and de-synchronization in the coupled neurons bases on theory of nonlinear dynamics become a hot topic. Synchronization and de-synchronization of coupled Hindmarsh-Rose neurons is investigated in this paper. The paper is organized as follows:The first chapter mainly introduces the basic theory of neurons, Hindmarsh-Rose neuron model and the common kinds of chaos synchronization.In the second chapter, the hybrid synchronization of two neurons described by Hindmarsh-Rose neuron model via single variable drive-response control is investigated. The synchronization strategy which applies feedback and adaptive control is proposed. The feasibility of the synchronization method is analyzed. The numerical results show that the synchronization method can lead to anti-synchronization of partial variables while it causes synchronization of other variables, namely anti-synchronization and synchronization of two chaotic neurons can be achieved by single variable control. We also find that the anti-synchronization of two chaotic neurons can be achieved when two control variable are applied. In the third chapter, the synchronization is investigated in a two dimensional Hindmarsh-Rose neuronal network by introducing a global coupling scheme with time delay, where the length of delay time is proportional to the spatial distance between neurons. We find that the time delay always disturbs synchronization of the networks. When both the coupling strength and length of time delay per unit distance (i.e., enlargement factor) are large enough, abnormal oscillations of neurons are observed due to the time delay. Furthermore, the abnormal oscillations of the symmetrical neurons form inverse phase so that the large coupling strength and enlargement factor lead to the de-synchronization of the neuronal network. The complete and intermittently complete synchronization of the neuronal network are observed for the right choice of parameter. The physical mechanism underlying these phenomena is analyzed. |
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