Recurrence quantification and bifurcation analysis of electrical activity in resistive/memristive synapse coupled Fitzhugh–Nagumo type neurons

Abstract

Temporal response of excitable individual and coupled different neuronal circuits i.e., Cell-I and Cell-II, of Fitzhugh–Nagumo type have been numerically simulated with a view to understand and characterize the complexities of involved dynamical processes. FHN neuronal circuit Cell-I and Cell-II have been shown to exhibit supercritical Hopf bifurcation, when excited by an external steady stimulus. For time varying sinusoidal excitation, the temporal action potential behavior of these neuronal circuits, when analyzed using measures of recurrence quantification analysis (RQA) and bifurcation diagram reveals period-1, period-2, multi-periodic, chaotic and reverse period doubling characteristics as observed earlier experimentally in giant squid axon and other biological cell assemblies. Phase portrait, bifurcation diagrams and recurrence plot (RPs), of (i) unidirectional and (ii) bidirectional coupled FHN Cell-I and Cell-II, through a gap junction resistor, suggest the possibility of transition to intermittent state besides the transition of respective action potential from periodic to multi-periodic to chaotic state in an ordered or disordered fashion, depending on values of system parameters that control the complexities. Further, for both the configurations (i) and (ii), synchronization of FHN neuron Cell-I with Cell-II is also shown to occur for large values of coupling parameter, ξ. The dynamical effect of electromagnetic radiation on individual FHN neuron circuits has also been investigated using a flux controlled memristor that couples the magnetic flux with the individual FHN neurons. Phase portrait, bifurcation and RQA analysis have also been used to characterize the electrical activities of excitable cell assemblies involving memristive synapse coupled FHN neuronal Cell-I and Cell-II in settings (i) and (ii) respectively.