Chaos break and synchrony enrichment within Hindmarsh–Rose-type memristive neural models

The fluctuation of ions concentration across the cell membrane of neuron can generate a time varying electromagnetic field. Thus, memristors are used to realize the coupling between the magnetic flux and the membrane potential across the membrane. Such coupling results from the phenomenon of electromagnetic induction in neurons. In this work, we numerically show that the electromagnetic induction phenomenon can firstly suppress chaotic states in a neural setups and secondly enrich neural synchrony in a system of two coupled neurons. By means of the bifurcation diagrams on maximum Lyapunov exponent and interspike interval, we show that increasing in memristor strength delocalizes first, then fully suppresses chaotic states in a single neuron. In a system of two electrically coupled Hindmarsh–Rose-type neurons, we realize that increasing in memristor strength gradually reduces the threshold value of electrical synaptic coupling strength above which a transition to synchronized states is achieved. The transition to synchronized states are determined either by the sign of the maximum transverse Lyapunov exponent or by the magnitude of the synchronization factor. Our results suggest that chaos break in a neurons group by electromagnetic induction phenomenon might automatically release neural synchrony which is involved in information processing and many seizures in the brain.