Nerve Discharge Of A Class Of Random Rhythms And Array Hair Chaos Dynamics Mechanism Study

In the past few decades, a branch of natural science, neurodynamics has been emerging from combination of neuroscience and nonlinear science. Many kinds of nonlinear behavior have been frequently observed in the nervous system, whose firing patterns play very important roles in neurodynamics. As the characteristic of nervous system that can receive, transmit and process the information by abundant neural firing. Periodic, chaotic and stochastic neural firing rhythms are their general basis forms. Therefore, to identify non-periodic neural rhythm to be chaos or stochasticity has been an important scientific thesis.In this dissertation, Identification of a stochastic neural firing rhythm lying in period adding bifurcation and resembling chaos is studied, based on the theory of nonlinear dynamics, combining the knowledge of mathematics, physics and life sciences, by making a theoretical model and using of computer numerical simulation method. It reveals the deterministic dynamics and stochastic dynamics are detected in the rhythm. And non-smooth features of intermittent neural bursting and spiking firing are studied. It reveals their respective non-smooth features by comparing with type-I and type-V intermittency.In Chapter1, the concept and development of nonlinear science and application of nonlinear dynamics research in nervous system are introduced at first. Second, it tells the status and progress of the Chaos Theory and some research in nervous system, including domestic scholars played an important role in promoting the chaotic development of the neural firing. Finally, content of the dissertation are introduced.In Chapter2, some concept of basic theoretical knowledge are introduced, contents include excitable cells and their type, the concept of neurons, type of neurons and their structure, concept and its mechanism of neuron action potential, the mathematical model of neuron, time series analysis, the correspondence of nonlinear dynamics and biology and so on.In Chapter3, A kind of non-periodic spontaneous firing pattern, whose behavior is transition between period-k burst in a string and period-k+1burst in a string (k=1,2) and lying between period-k bursting pattern and period-k+1bursting pattern, was discovered in the experimental neural pacemaker. The deterministic structures of the firing are identified by nonlinear prediction and first return map of the interspike intervals (ISIs) series. The co-existence of the period-k bursting and period-k+1bursting is manifested in the deterministic theoretical neuronal model, Chay model. Non-periodic firing patterns similar to the experimental observation are simulated in the co-existing parameter region, implying that the firing pattern is transition between two kinds of bursts induced by noise. A binary series can be acquired by transforming two kinds of bursts to symbols0and1, respectively. The stochastic dynamics within the transitions between two kinds of bursts are detected by probability analysis to the binary series. It shows that the rhythm is stochastic firing with deterministic structures instead of chaos.In Chapter4, the features of period-3intermittent chaos neural bursting and spiking firing are studied by numerical simulation in deterministic Chay model when parameters are fixed. Comparing these two intermittency scale law with type-Ⅰ intermittency scale law produced smooth system and type-Ⅴ intermittency scale law produced non-smooth system, their scale law ranged between type-Ⅰ intermittency and type-Ⅴ intermittency are found by calculating the first and the third return map of two kind of intermittent chaos and the average laminar length and least squares linear fitting.In Chapter5, conclusion of this dissertation is provided.