Study On Synchronizations Of Coupled Neuronal System

Nervous system in the head enables people to complete a variety of highly complex activities, such as feeling, sport, learning, thinking, memory, speaking, and so on. The brain function can be achieved through the huge quantity of neuron and the complicated connections among neurons. The higher advanced the living being becomes, the more neuron number it has. The neuron number in the living system from plants to animals as well as from lower organisms to higher ones increases exponentially. The connections among neurons become more complex and diverse. This is why human beings have language and thinking. It is very significant to investigate how the nervous system achieves the thinking, consciousness, conditioned reflex and other activities by controlling and regulating the activity of neurons in subsystem.Neurons are the basic structural and functional units of the nervous system. Action potential (electrical impulse) is the basic way of signal transmission. Individual neurons can not implement the space-time encoding for continuous electrical pulses. Only the neuron population with specific connections can complete the reception, integration and transmission of signal. In other words, signal transmission depends on the operational modes of neuron populations in the nervous system. The operational modes mainly apply the common synaptic current to achieve synchronization among neurons. The synchronization of neuron population is a fundamental natural phenomenon of synchronization. Investigation on synchronization among chaotic neuron oscillators is directly relates to our understanding of human brain function and it can help us to reveal the principle of information storage in the mammalian brain. At the present, investigations on synchronization of neuronal network mainly focus on the neuronal network with small number of neurons and ring or chain topology. The synchronization of two-dimensional (2D) neuronal network with a lot of neurons and How to improve the efficiency of synchronization by regulating coupled modes are still lack of adequate research.It is well known that the brain cortex and visual nervous system are hierarchical couplings. There are the cascade information transfers. The brain and nervous system can adjust the coupling strength of a given connection through unknown mechanisms. Based on above results, the synchronizations of a two-dimensional (2D) neuronal network are investigated by using the dynamical model of Hindmarsh-Rose (HR) neuron. In addition, the synchronizations of the one-dimensional neuronal network with ring structure under the control of the formation of a neuron information is studied. Some results are obtained. This paper is organized as follows:The first chapter is the overview. The structure and type of neurons, the formation mechanism of the electrical signals of neurons, the types of encoding, the classification of neuron synaptic, the mathematics models of neurons with electrical activity, the synchronization of the simple neuronal network are briefly introduced.The second chapter focused on our first research work. The synchronization of a two-dimensional (2D) neuronal network is investigated. In order to know the effects of different types of coupling on the synchronization of a network, we propose three coupling schemes. They are the general feedback coupling, the hierarchical feedback couplings with and without local mean field. The numerical results show that when the neighbor coupling strength is small, the hierarchical feedback couplings with and without local mean field can achieve local and global synchronizations of the network, whereas the general feedback coupling cannot achieve global synchronization. Different couplings generate different patterns in the corresponding network, so that the processes of the transition from asynchronization to synchronization in the networks are different. With the increase of coupling strength, the synchronization in the network with the general feedback or hierarchical feedback couplings is suddenly established, and the networks exhibit different coherent patterns that are aperiodic before the global synchronization occurs. However, the network with hierarchical feedback couplings and local mean field exhibits the different synchronous processes. The neurons in the same layer first achieve the transition from bursting synchronization to global synchronization, leading to the formation of target wave. Then, the synchronization region gradually expands from the center of the network. Finally, the whole networks can achieve synchronization. These results show that the lossless signal transmission can be achieved only if the appropriate coupling is applied. In addition, we find that the hierarchical feedback coupling with local mean field can facilitate synchronization.The third chapter focused on our second research work. The center neuron’s information-induced synchronization of the one-dimensional neuronal network with ring structure and the neighbor feedback coupling is studied. Since neurons in the brain can modulate the coupling strength between neurons through neuronal synchronization (i.e., phase), we introduce a center neuron in the neuronal network, supposing that the center neuron can provide its status information to other neurons and other neurons can modulate the coupling strength between the neighbor neuron and itself by applying the status information of the neighbor and center neurons. Several adjusting schemes of coupling strength are proposed. It is found that the more information neurons get, the smaller the coupling strength the global synchronization of network needs, and the higher synchronization efficiency the neural network has. At this time, the neighbor coupled network can achieve global synchronization when coupling strength is small. If there is no information provided by the center neuron, coupling strength needs to be increased a hundred times for the neuronal network to achieve complete synchronization. In order to achieve the global synchronization of the network, coupling strength will increase dramatically when the number of neurons increases. On the contrary, if there is the information provided by the center neuron the increase of the neuron number only lead to a little increase of coupling strength, at which the network can achieve the global synchronization, showing good robustness of the network expansion. And we find that the synchronization processes of the networks with and without the information of the center neuron are different when the coupling strength gradually increases. When there is no the information of the center neuron, the network achieves the global synchronization through long-range coherent. When neurons in the network can get the information of the center neuron, the network realize global synchronization through the paroxysmal synchronization if neurons obtain less information from the center neuron, otherwise the network realize the global synchronization mainly through the expansion of synchronization area.