Fast and slow dynamical behaviors of delayed-coupled thermosensitive neurons under electromagnetic induction

Abstract

This paper studies the dynamics of a thermosensitive neuronal network with delayed chemical synapses under electromagnetic induction. The stability and different bifurcations of the network are analyzed. Abundant and interesting bursting oscillations are explored, such as point–point bursting, cycle–cycle bursting, point-cycle bursting and cycle-point bursting oscillations. Time delay plays important roles in the system dynamics, including the amplitude of the spiking state and the delay interval of the subcritical Hopf bifurcation. The average Hamiltonian energy is considered to estimate the synchronized behaviors between neurons, such as intermittent synchronization. As the strength of the chemical synapses varies, asynchronous behaviors, intermittently synchronized and fully synchronized states are observed. The influences of the feedback strength gain of external stimuli induced by electromagnetic induction and temperature coefficient on the synchronized dynamics are discussed. Based on the exponential function circuit, time delay circuit and transfer function circuit, the circuit platform of the network is constructed. The responses of the circuit reach an agreement with the obtained results.