Bifurcation In Neuron Models Exposed To External Electric Fields

As the fundamental structural and functional unit of the nervous system, neuron plays a pivotal role in the neural information processing. This thesis investigates the effects of external electric fields (EEF) on neuronal system, which is directed toward offering references for studying the impact of EEF on kinds of neural functions from more macroscopic perspective.On the basis of analyzing the electrophysiological properties of cell membrane when exposed to EEF, this thesis firstly establishes a neuronal model under the effects of EEF. And then the thesis, with the bifurcation theory, obtains the detailed bifurcation structure of Hodgkin-Huxley (HH) Model and Morris-Lecar (ML) Model under DC electric fields; and identifies the parameter regions of multistabilities and reveals their bifurcation mechanisms. The thesis explores the dynamics of HH neuron under AC electric fields with different amplitudes and frequencies, and finds firing sequences of period-adding without chaos and alternated mode locking and chaos (or quasi-period), etc. as well as their dynamic transitions, by virtue of Poincare section, ISI, and average firing rate; The Anorld diagram in amplitude-frequency parameter space reveals the decoding mechanism of firing patterns onto stimulation inputs.Through analyzing the bifurcation of ML neuron under EFF, the thesis finds four different excitability and spiking properties, which can be converted mutually only by changing a single parameter of EEF. Then, the thesis establishes three minimal bursting models based on ML model and provides the general laws of the changes of bursting characteristics by adjusting model parameters.In consideration of the importance of neuronal synchronization, the thesis, with the phase reduction method, studies synchronization dynamics of two coupled neurons (spiking or bursting ones) under electrical or chemical synapses; and obtains the influence law of stimulation current, electric fields, coupling properties and strength on the synchronizition dynamics. The time delay is unavoidable in information transmitting in nervous system. The research concludes that different time delays act a role of synchronization entrainment and desynchronization, and also can give rise to multistability of synchronization.The above research results contribute to revealing and explaining nosogenesis of diseases caused by electromagnetic fields, and thus provide a theoretical support for prevention and treatment of neurologic and brain disorders, and also provide theoretical guidance for formulation of electromagnetic environmental standards and clinical medical application of electric stimulation.