Coexisting Firing Patterns And Memristor Synapse-coupled Synchronization In Morris-Lecar Neuron

Neuron is the most basic constituent and functional unit of the nervous system,and it is the research basis of neuroscience.Due to its simplicity and rich firing behavior,Morris-Lecar neuron model has attracted extensive attention since it was proposed.The electrical activity of neurons can be affected by electromagnetic radiation,and the flux-controlled memristor can act as the coupling synapse between the neuronal cells.Therefore,based on the research of chaotic bursting dynamics and coexisting multistable firing patterns in the three-dimensional Morris-Lecar neuron model,this paper constructs a memristor synaptic-coupled Morris-Lecar bi-neuron network,and discusses its dynamical behavior by means of simulation analysis and digital circuit experiments.First,we investigate the chaotic bursting dynamics and coexisting multistable firing patterns in a three-dimensional autonomous Morris-Lecar neuron model.For some specified model parameters,by means of numerical simulation,diverse forms of chaotic bursting,chaotic tonic-spiking and periodic bursting behaviors are uncovered in the Morris-Lecar neuron model.On this basis,the fold/Hopf bifurcation set of fast subsystem is constructed theoretically,and the bifurcation mechanism of chaotic bursting behaviors is powerfully explained.In addition,through numerically plotting the attraction basins related to the initial states,coexisting multistable firing patterns are demonstrated in the 3D Morris-Lecar neuron model.Finally,a digitally circuit-implemented electronic neuron is generated and its experimentally captured results faultlessly validate the numerical plots.Secondly,based on the three-dimensional autonomous Morris-Lecar neuron and memristor synapse,a memristor synapse-coupled bi-neuron network was constructed.Coexisting firing activities in the heterogeneous memristive bi-neuron network are explored by numerical simulation method,upon which the initial-induced infinitely many firing patterns are disclosed,indicating the emergence of the initial-induced extreme multistability.Furthermore,synchronous firing activities in homogeneous memristive bi-neuron network are investigated using the time sequences,synchronization transition states,and mean synchronized errors.The results demonstrate that the synchronous firing activities are associated with the induction coefficient and specially associated with the initial values of memristor synapse and coupling neurons.Finally,an FPGA-based electronic bi-neuron network is designed to experimentally confirm the memristor initial-induced coexisting firing activities.