Research On The Synchronization Induction And Regulation Mechanism Of Complex Time-delay Coupled System

Synchronization is one of the typical expressions of complex system movement, for a nerural system, it refers to the individual neuron of the system discharge synchronously, or their discharge rhythm maintain a strong correlation or display some kind of clustering behavior. There are sufficient evidences show that there is a strong inherent relationship between the sensory, cognitive, memory as well as so on in nerural system and the synchronous discharge behaviors of the neural network. Therefore, the problem of coupled synchronous oscillation in nerural system is the key in the research of neural information processing. The main work and achievement of this dissertation are shown as follows,(1) Based on self-synaptic coupled neuron model, the influence of time-delayed signal linear and nonlinear feedback on the firing patterns are studied in an individual neuron, it is found that self-synaptic coupling makes the Interval Spike Interval(ISI) much more complex than that in a basic neuron’s, many new discharge modes appear, in addition, the transfer of the firing patters are speeded up under time-delayed signal nonlinear feedback; in the research on the transmission characteristics of a neuron, it is shown that appropriate weak background noise, moderate sinusoidal excitation frequency and amplitude are all conducive to the neuronal signal optimal transmission.(2) On synchronization feature with asymmetric structure coupling neuronal system, it is discovered that the time-delay scope and coupling strength for the synchronization correlated positively under unequal time-delay, the time-delay difference doesn’t make a clear distinction between the two individual ISI bifurcation diagrams in the two coupled neurons, therefore, the superficial difference of the system synchronous dynamics is not obvious for the unequal time-delay feedback. In the asymmetrical current incentives under asymmetric electric coupling system, the system can only almost completely synchronized in specific area of the interval between a single neuron firing patterns for the two individual stimuli current before coupling, but the intervention of time-delay feedback, together with the change of the coupling strength can make the coupled system not only almost completely synchronized within anywhere in the front area, but also even outside of it.(3) With basic principles of stability theory and Lyapunov function, the condition of the complete synchronization of coupled neuronal system with chemical synapses is studied theoretically. The boundedness of the model solution is proved by analytical approach first, then, based on the negative definition of quadratic of the constructed Lyapunov function come from the simplified error differential equation of the system synchronization manifold, the sufficient condition of the complete synchronization is proposed.(4) The influence of noise on the complete synchronization in a model neuronal system is investigated. It is illustrated that two isolated neurons with different initial conditions can discharge complete synchronously when the noise intensity is large enough, and for a smaller calcium ion reversal potential, the uncoupled neuronal system could be induced to a complete synchronization state under smaller critical noise intensity; the synchronization characteristics of the two coupled neurons are discussed by analyzing Similarity Function of the two membrane potentials of two electrically coupled neural system, the results show that two coupled neurons can be synchronized under very small noise intensity even in the case of weak coupling, which proves that noise can promote the complete synchronization; the overall trend shows that the critical noise intensity which can induce the complete synchronization in coupled system decreases with the increase of calcium ion reversal potential, and this is just opposite to the situation in the uncoupled system, this proves that the increase of calcium ion reversal potential is helpful for the synchronization enhancement in coupled neuronal system as a whole.(5) The synchronization target mode decision and transition mechanism are investigated, the results show that the synchronous states of the small-world neuronal network is completely determined by its external incentive current, have nothing about the coupling strength as well as the connection probability; with two different amplitude stimuli current, only almost complete synchronization can be achieved, and the firing patterns of the synchronized small-world neuronal network only distributes the interval with two endpoints, which just correspond to the two modes in a single model neuron with these two kinds of amplitude stimuli current, the specific firing pattern is decided by the proportion of the neuron numbers, which are stimulated by these two kinds of different amplitude stimuli current respectively.The achievements of this dissertation will deepen the understanding about the functions of synchronous discharge in neural information processing and handling, and then, disclose the mechanism of synchronization in neuronal system with the effects of time-delay and noise, continue to explore the mathematical mechanism of senior brain functions and its lesions, consequently, theoretically support the neurophysiology researches and the clinical treatments. The conclusions of this work, furthermore, also have reference value to the vibration control of the mechanical system.