Influence of memristor and noise on H–R neurons

Abstract

We study the effect of electromagnetic induction on improved Hindmarsh–Rose neuron model with flux-based memristor terms. The electrical activity of single neuron and of coupled neurons under the influence of quadratic memristor term and the influence of noise on isolated and coupled neurons are analyzed. Our results confirm that, when noise is added, the oscillation death is achieved for relatively smaller magnitudes of external steady current and it also leads to the inhibition of bursting under periodic current. The functional responses of membrane potential of single as well as of coupled neuron exhibit bursting, tonic, quiescent and even suppression of oscillations under quadratic flux induction, as external current is varied. The suppression of oscillation for higher current in the presence of quadratic flux is quite distinct from the cubic flux case where increase in current exhibits continuous spiking. The variation of Hamilton energy against external current confirms the existence of quiescent state. The bifurcation plot of interspike interval versus current in the presence of external quadratic flux is denser than that of cubic flux-based electromagnetic induction which indicates a higher degree of aperiodicity. The plot of Lyapunov exponent versus characteristic parameter exhibited anisotropy and chaotic nature for the dynamics of the neuron. For coupled neurons, the synchronization patterns shows periodic-, chaotic-, and tonic-type transitions. For certain noise intensity and coupling strength, the oscillation death is also exhibited by the coupled neurons. For the exponential flux-controlled memristor, the coupled neurons exhibit the synchronizations with dynamics of antiphase, periodic, chaotic, and of oscillation death. The plot of transverse Lyapunov exponent of coupled neurons establish that the system is chaotic for certain values of coupling constant.