Chaos, Synchronization And Control Of Neurons

The neurons are believed to be the key elements in the signal processing of neural system.The generation and transmitting of neural information are nonlinear, so the dynamic performances of individual or coupled neurons get the main focus in the neuroscience research. It was found that the neurons can fire in different patterns, such as chaos and quasi-period, and coupled neurons can fire synchrously under external stimulation.Firstly in this dissertation, the cable model of a cylindrical cell in external electrical stimulation is established and the recovery variable based on the Fitzhugh-Nagumo (FHN) model is introduced to describe the slow process of firing. Then, the dynamic performances of single neuron under external electrical stimulation with varied frequency have been analyzed in detail. The complex nonlinear phenomenons such as limit cycle, quasi-period oscillation and chaos were found in the simulation, and the chaos of active potential is demonstrated by Lyapunov exponent, power spectra and phase plane.The synchronization of coupled neurons plays the main role in the process of neural informations tansmiting, so the research on the synchronization of neurons coupled with gap junction is one of the main contents of this dissertation. The model of two or more neurons coupled with gap junction is established on the base of single neuron model to study the influence of the coupling strength of gap junction on the synchronization and the sufficient condition of synchronization is given.Time delay is the main fator to affect the informations transmitting among neurons, so this dissertation is also dedicated to study the synchronization of time-delay coupled neurons. The model of time-delay coupled neurons has been established to study the effects of time delay and the coupling strength on the synchronization and the sufficient condition of delay coupled neurons synchronization which relates to the time delay and coupling strength is given.The chaotic synchronization in neurons may imply some neural diseases or the improvement of these diseases. As the external stimulation can change the sysnchronization in neurons, in this dissertation, the Lyapunov control, Backstepping control and variable universe adaptive fuzzy control have been applied to synchronize the neurons. The parameters of neuron model and the external condition of neuron are nonlinear, so the fuzzy approximation and H_∞control are employed to guarantee the robustness of the system.The results of simulation demonstrated the validity of the theoretic analysis and control algorithms refered to above.The conclusions of this dissertation can benefit the researches on the brain, the quantitative analyze of acupuncture and the treatment of some neural disease.