Researsh On The Diversity Of Firing Patterns And Bifurcation Characteristics Of Coupled Neuronal Systems Based On The Influence Of Multiple Parameters

The study of neuronal systems from the perspective of non-linear dynamics can not only help us to explain some complex behaviours in neuroscience,but also provide new theoretical basis for practical physiological experiments and disease treatment.Neurons are the smallest units in the nervous system,and individual neurons are unable to encode and transmit information.Neurons must be coupled synaptically to form complex neural networks to process and transmit information.While studies based on individual neurons can describe the firing behaviour of neurons well,the dynamics of coupled systems can better reflect the collective behaviour of neural networks.In addition,due to the prevalence of time lag and electromagnetic induction effects,it is crucial to consider the effects of various factors on the system.The main contents of this article are as follows:In the first part,the stability of the equilibrium point of a single Chay neuron system is firstly analysed.Secondly,the types of equilibrium points of the system under the influence of coupling strength are considered and numerical simulations are carried out.Then,the bifurcation analysis with single and two parameters is carried out to obtain the rich dynamical behaviour under different parameter matching.Time lags are also considered,and the discharge patterns of the system are discussed for both symmetric and unilateral time lags.Finally,the synchronisation of the system is analysed by statistical methods such as correlation coefficients and similarity functions,which show the synchronisation process of the system more clearly.In the second part,the dynamical properties of the chemically coupled Chay neuron system are discussed.Using C programming simulations,ISI bifurcation diagrams were obtained for the effects of parameters such as conductance,synaptic reversible potential and synaptic threshold.It was found that two identical neurons were chemically synaptically coupled and that the firing pattern of the system was strongly influenced by the strength of the coupling at the same initial value.An increase in coupling strength leads to an increase in bursting discharge period and region.In particular,with the synaptic reversible potential and synaptic threshold as bifurcation parameters,the spiking discharge and bursting discharge regions are significantly increased and the chaotic region is compressed.Finally,for chemical synaptic coupling,the synchronization of the system was also analysed using similarity functions,and it was found that the system showed a transition process of non-synchronous,bursting-synchronous,non-synchronous and finally resting synchronous.In the third part,on the basis of the Chay neuron model with the introduction of magnetic flux.Firstly,the equilibrium point and stability of the system are investigated by Matcont simulation,and it is found that the bifurcation behaviour of the system such as supercritical Hopf bifurcation and subcritical Hopf bifurcation occurs with the change of parameters.Secondly,the bifurcation and discharge patterns of the neuronal system are explored by drawing the ISI bifurcation diagram of the system.Finally,the effect of multiple parameters on the synchronisation process of the coupled system is further discussed using the statistical properties of the correlation coefficient and the synchronisation parameters.In the fourth part,based on Chay neurons,used electrochemical hybrid synapses to construct a network of ring and two-dimensional lattice neurons,and investigated the effect of the number of left and right connected neurons in the ring-shaped network on the firing behaviour of the system.It was found that as the number of left-and right-connected neurons increased,the cluster discharge period of the system increased,and in particular,tonic discharge regions appeared in the two-parameter plane of the system.Afterwards,the spatio-temporal waveforms of the system are obtained by programming simulations and combined with statistical synchronization factors to better explore the whole synchronization process of the network system with the variation of coupling strength.Secondly,by analyzing the bifurcation diagrams of Afterwards,the spatio-temporal waveforms of the system are obtained by programming simulations and combined with statistical synchronization factors to better explore the whole synchronization process of the neural networks with the variation of coupling strength.Then,it is found that as the size of the lattice increases,the peak discharge region becomes chaotic and the plane area occupied by each cycle of the cluster discharge region gradually decreases.Finally,the target waves induced by the stimulation current in the central region are discussed,further enriching the spatio-temporal dynamics behaviour of the Chay neuron system.