Synchronization Control Of A Class Of Neuron Systems And Its Application In Secure Communication

In the process of information processing and operation,the nervous system is closely related to the discharge activity of neuron membrane potential,which leads to the transmembrane transport of related ions.From Kirchhoff's law,it can be concluded that the transmembrane motion of the accompanying ions in neurons will produce a variety of time-varying electromagnetic fields,in which case the electromagnetic field can further regulate the transmission of neural information and the discharge pattern of neurons.Therefore,in-depth study of the dynamic characteristics and application of neuron model under electromagnetic induction has important practical reference value.Firstly,based on the theoretical analysis of saddle node bifurcation and Hopf bifurcation,the discharge activity and bifurcation characteristics of four-dimensional HR neuron model under electromagnetic radiation are studied,with emphasis on the saddle node bifurcation and supercritical Hopf bifurcation under the change of internal parameters.In detail,by exploring the influence of external stimulating current I on the existence and stability of equilibrium points of the model,theoretical studies show that there are multiple equilibrium regions in the model,which reflects that the model has rich nonlinear characteristics.Based on the analysis of saddle node bifurcation,the distribution of multi-valued equilibrium region and critical saddle node of the model is discussed.Then the Hopf bifurcation behavior and bifurcation types of the model are studied,and the discharge behavior of the model is numerically simulated,and the results of bifurcation theory are verified.In addition,based on a large number of time response diagrams,single-parameter bifurcation diagrams and two-parameter bifurcation diagrams and other numerical simulation tools,the discharge characteristics and bifurcation laws of the system are discussed in detail.Then,based on the flux neuron system,the bifurcation structure of the flux HR neuron model in the two-parameter plane is explored,and it is found that the system has period-doubling bifurcation with chaos and period-adding bifurcation without chaos.By using the adaptive control method,the synchronous control of the HR neuron model of the electric synaptic coupling flux is studied.By applying the control term to the slave system,the synchronous control of the discharge states of different periodic clusters between the master and slave systems is realized.Thus,it provides a useful discussion for understanding the discharge activity of flux neurons and the migration of membrane voltage.Finally,a HR neuron system with memristor coupling is established by using Lyapunov global stability theory.Under different initial conditions,through the reasonable design of adaptive controller and parameter identification law,theoretical analysis and a large number of numerical simulations show that the coupled system can gradually tend to the synchronous state efficiently.This shows that the controller has good stability and self-adaptability.In addition,the coupling system is applied to the secure signal transmission,and the research shows that a good numerical effect is obtained,which will provide an important reference for the nervous system to encrypt the image and transmit the secure signal.