The Chaos And Synchronization Of Nerve Fibre In External Electrical Field

With the development of chaos theory, it has been applied in a lot of areasincluding biomedical engineering. The research on the nerve fiber excitation byelectrical stimulation plays an important role in the fields of neuroscience, healingproject and so on. The application of chaos theory to it can be divided into two maingroups. One is to analyze the experiment data with the methods of chaos theory, theother is to establish the model of neuron and investigate the dynamical behaviors ofnerve fiber. In this paper, the dynamical behaviors of an independent neuron in externalelectrical stimulation and the synchronization between two coupled neurons are themain focuses. First, the cable model of a cylindrical cell in external random directionelectrical stimulation is established. Because of the nonlinearity of membraneconductance, the recovery variable based on the Fitzhugh-Nagumo equations isintroduced to this model. The frequency of the electrical stimulation is varied toinvestigate the dynamical behaviors of the neuron. The complex nonlinearphenomenon such as limit cycle, phase-locked and chaos were found in the simulation.The chaos is confirmed by Lyapunov exponents, power spectra and phase plots. Thesynchronization between two coupled neurons plays an important role in revealingcommunication pathways in neural system. Basing on the previous cable model, themodel of two neurons coupled with gap junctions is established. The influence of thecoupling strength of gap junctions is the major focus. The sufficient condition for thecomplete synchronization is given in the end.