Firing Pattern And Memristor Synapse Coupling Synchronous Behavior In Chay Neuron Model

The Chay neuron model is derived from the classical Hodgkin–Huxley neuron model.Due to the great importance for its firing patterns of the outward current carried by K⁺ion and the inward one by Na⁺and Ca²⁺ions in the three-dimensional(3D)Chay neuron model,the transmission of firing patterns in connection with the maximal conductances of K⁺ions channel and mixed Na⁺–Ca²⁺ions channel can be explored for better explain the mechanism of their action on the electrical activity in Chay neuron model.Besides,the synchronous behavior of coupled biological neurons plays an important role in biological information transmission and encoding.Thus,the exploration of memristive synapse–coupled neuron synchronization has positive guiding significance to solve some practical problems such as treating disorders of the brain.In this paper,the maximal conductance g_I of mixed Na⁺–Ca²⁺channel and maximal conductance g_K,V of K⁺channel related firing patterns are explored in the 3D Chay neuron model and the synchronous behavior of memristive synapse–coupled are disclosed.Employing the phase plane plot,time sequence,bifurcation diagram,Lyapunov exponent,spectral entropy complexity diagram,2-D dynamical map and 0-1 test for the theoretical analysis and numerical simulated ones,the transmission of firing patterns depending on the maximal conductances of K⁺ions channel and mixed Na⁺–Ca²⁺ions channel is numerically revealed,including the periodic and chaotic bursting behaviors and chaotic spiking behavior.Then,we utilize the fast–slow dynamics analysis to reveal the generating mechanisms of the spiking/bursting firing patterns.The mechanisms for periodic fold/fold bursting,periodic and chaotic fold/homoclinic bursting,and chaotic spiking behaviors in the Chay neuron model are expounded and elaborated.Employ a memristor with threshold memductance as a bi–directional synapse to couple two identical 3D Chay neurons to characterize the electromagnetic induction induced by membrane potential difference of the two neurons,a memristive synapse–coupled Chay twin–neuron network is then built.The synchronization behavior of four typical firing patterns in memristive synapse–coupled neuron network was numerically simulated and analyzed by ultilizing time sequence,synchronous transition state and mean synchronization error analysis method.The synchronization behavior depending on the coupling strength and initial condition of the memristor in the homogeneous Chay neurons network are investigated.Furthermore,based on a field programmable gate array(FPGA),a digitally circuit-implemented electronic neuron is made,upon which experimental measurements are executed.The experimental captured results further confirm the theoretical analysis and numerical simulated ones.