Hindmarsh-Rose neuron model with memristors

We analyze single and coupled Hindmarsh-Rose neurons in the presence of a time varying electromagnetic field which results from the exchange of ions across the membrane. Memristors are used to model the relation between magnetic flux of the electromagnetic field and the membrane potential of interacting neurons. The bifurcation analysis of Hindmarsh-Rose neurons has been carried out by varying the modulation intensity of induced current on the membrane potential. Many important dynamical behaviors such as synchrony, desynchrony, amplitude death, anti-phase oscillations, coexistence of resting and spiking state, and near death rare spikes are observed when the neurons are coupled using electrical and chemical synapses. In all cases the transverse Lyapunov exponents are plotted to observe the point of transition from desynchrony to synchrony. The memristor based analysis on neural networks can contribute to biological system modeling and can be used as a synapse in hardware of artificial neural networks.