Spatiotemporal Dynamics Behavior Of The Three Types Of Neural Network Research

Neuronal system is a huge and complex information network, which is connected by thousands of neurons. This system plays a crucial role in the motion control and cognitive function including perception, study, memory, thinking, etc. Synchronization and spiral wave are the major forms of neuronal clusters and play a very important role in the neuronal networks. In addition, noise is an inevitable factor in real neuronal systems, which plays an important role on spatiotemporal dynamics of neuronal networks. Therefore, it should be performed an important work at the present time that the spatiotemporal dynamics of neuronal networks will be studied theoretically and got in-depth knowledge. Considering the fact that neural information encoding is realized by various firing rhythm patterns of neurons, different firing rhythm patterns reflect that neurons have different nonlinear dynamical properties. Thus, concerning the dynamical properties of network unit is an important question in real neuronal systems.By the nonlinear dynamical theories and method, we study the spatiotemporal dynamics of three types of neuronal network by numerical simulation. Three types of neuronal network:two coupled neurons with coexisting behavior, the neuronal network composed of three neurons with actual biological significance (stomatogastric ganglion, STG), and the large-scale neuronal network composed of class â…  or â…¡ excitable neurons respectively. Firstly, synchronization and synchronization transitions of coupled neurons with co-existing spiking and bursting are studied. Secondly, firing rhythm and three-phase activity pattern in the pyloric system of the crayfish STG are simulated in two-compartmental model. Thirdly, the spatial patterns (spiral wave) and multiple spatial coherence resonances induced by noise or diversity in neuronal networks composed of class I or II excitable neuron are studied. These results offer the theoretical foundations for understanding on information processing and transmission of neuronal systems deeply, either for the diagnosis of physiopathology. Besides, they can promote development of nonlinear dynamics.The goal and significance of this study are introduced firstly in Chapter1. Then, development and advances in researches of neurodynamics and neuronal network are introduced. Following these introductions is the main work of this dissertation. The neuron, neuronal network, and corresponding mathematical models, nonlinear dynamics of neural excitability and firing rhythm of neuron in neuronal system, and spatiotemporal of neuronal network are introduced in Chapter2.The synchronizations and transition of neuronal network, which is composed of neurons with co-existing behaviors, are introduced in Chapter3. The properties of co-existing attractors of spiking and bursting are manifested in Leech neuron model. Choosing three control parameters Vk2shift in co-existing interval of spiking and bursting, synchronization states and transitions processes corresponding to three control parameters are simulated in two coupled Leech neurons whose behaviors are the different ones of co-existing attractors respectively. By comparing the three processes of synchronization transition, several general changing regularities with respect to the decrease of control parameter can be acquired,(a) When coupling strength is sufficiently large, the complete synchronization behavior of coupled neural system can be changed from bursting to spiking when the control parameter decreases,(b) In three processes of synchronization, transition between synchronization sates of spiking and bursting becomes infrequent when the control parameter decreases,(c) Complete synchronization of spiking and synchronization of spiking become easier while the appearance of the complete synchronization of bursting and synchronization of bursting become more difficult, with respect to the decrease of control parameter,(d) For single neuron of neuronal network, the spiking pattern appears easily while the bursting pattern gets difficult with respect to the decrease of control parameter. The results are instructive to understand synchronization behaviors and its transition of the coupled system with co-existing attractors.The firing patterns of neuron and three-phase rhythm of the pyloric system in invertebrate crayfish are simulated in Chapter4. Firstly, we research and discuss the mechanism of neuron firing of two-compartmental model. And the rich firing patterns in pyloric of STG are simulated in neuron model with two compartments. Then, based on inhibitory synapses among LP (lateral pyloric), PY (pyloric) and PD (pyloric dilator)(inhibitory synapses from PD neuron to LP and PY neurons, inhibitory synapses from LP neuron to PD and PY neurons, inhibitory synapse from PY neuron to LP neuron), the pyloric network is constructed. Furthermore, three-phase rhythm LP-PY-PD is simulated. Several categories of three-phase rhythm observed in experiment can be simulated by regulating the coupling strength among three neurons. The results of the study show that three-phase rhythm depends not only on the uncoupled states of three neurons, but also on the couple strength among three neurons. The results are important to understand the dynamical mechanism of the real neuronal networks.The spatial patterns (spiral wave) and multiple spatial coherence resonances induced by noise or diversity in neuronal networks, which are composed of class I or II excitable neurons, are studied in Chapter5. In the central nervous system, neurons often work in the neighborhood of threshold, neurons are heterogeneous and noise is inevitable. We study the spatiotemporal behavior of network, which are composed of neurons nearby the neighborhood of threshold. Firstly, considered the homogeneous network composed of II excitable neurons through the white Gaussian noise, under different coupling strength, spiral wave is characterized by a transition back and forth between simple structure and complex structure, or the disordered structure when noise density increases. By calculating spatial structure function and signal-to-noise ratio (SNR), we find that the multiple spatial coherence resonances induced, and the multiple resonances are related to the transitions between simple patterns and complex patterns of spiral waves. Then, considering the heterogeneous network composed of II excitable neurons, spiral waves and multiple spatial coherence resonances in a two-dimensional neuronal network without or with noise induced by parameter diversity are simulated. In the absence of noise, multiple spatial coherence resonances and spiral waves are induced by parameter diversity. It is also found that the multiple resonances are related to the transitions between simple patterns and complex patterns of spiral waves. When noise is present, multiple spatial coherence resonances and spiral waves induced by the diversity are simulated. And the resonance degree induced by diversity is reduced with respect to the increase of noise density. The results suggest that there are many opportunities to select diverse strength or noise density to be utilized in the realistic excitable system, and shown that the noise influences the diversity-induced multiple spatial coherence resonances. Those provide reference for understanding spiral wave of visual network in biological experiment.Three types of neuronal network show different behavior of spatiotemporal dynamics, respectively. Here we demonstrated the behavior of spatiotemporal dynamics is complex; corresponding to the reality of biology and academic questions, this dissertation takes neurons with the corresponding dynamic behavior to build up the neuronal network with different coupling properties as the object of study.