Synchronization Of Coupled HR Neurons And It’s Application In Secure Communication

Neurons play a key role in the information processing of neural system, thegeneration and transmission of neural information have the nonlinear characteristics,so it is of great significance to study the nonlinear dynamics performances ofindividual or coupled neurons in the neuroscience. It is found that the neurons underexternal stimulation can fire in different patterns, such as quasi-period, chaos, andcoupled neurons’ synchronous spiking.Neurons are the basic structural and functional units of nervous system. Actionpotential is the basic way of signal transmission, the individual neuron can notimplement the encoding for continuous pulses, only can neuron populations completethe reception, integration and transmission of the signal. In this thesis, firstly, theHindmarsh-Rose model under external electrical stimulation was established, then,the dynamics performances of single neuron with different external stimuli wereanalyzed in detail. The complex nonlinear phenomena such as quasi-period burst andchaos were found through analyzing inter-spike interval sequences(ISI).In recent years, it becomes a hot topic to study the synchronization of neuronswith nonlinear dynamics theory and methods. In this thesis, the chaoticsynchronization of two electrically coupled Hindmarsh-Rose neurons with unknownparameters was studied with the nonlinear dynamics theory and methods. Based onthe Lyapunov stability theory, a nonlinear adaptive controller was designed andunknown parameters’ update rates set, which could achieve the synchronization of thetwo gap junction coupled Hindmarsh-Rose neurons with unknown parameters whenthe individual Hindmarsh-Rose neuron showed chaotic firing activity. The controllerwas robust to ionic channel noises and external disturbances. The numericalsimulation of coupled Hindmarsh-Rose neurons verified feasibility and effectivenessof the proposed controller.Finally, the nonlinear adaptive synchronization system was applied to secure communication, a system of secure communication was proposed based on thescheme. One channel of the system was used to transmit the output signal of thechaotic system nothing to do with the infromation signal and the other used totransmit the information-bearing signal. The simulating results showed effecticenessof the proposed secure communication system. The method is of some guidingsignificance for practical applications such as engineering chaotic communication.