Emergence of hidden dynamics in different neuronal network architecture with injected electromagnetic induction

Abstract

The diverse firing responses in a single neuron model as well as in a neuronal network play a major role in understanding the collective neuronal dynamics. In this paper, we consider an excitable slow-fast memristive model and study its various intrinsic dynamics by allowing a periodic external stimulus. The single model exhibits various types of spiking, bursting, mixed-mode oscillations (MMOs), and mixed-mode bursting oscillations (MMBOs) depending on the amplitude and frequency of the periodic injected current. Corresponding bifurcation analysis reveals the existence of supercritical and subcritical Hopf bifurcations in the system depending on the major predominant parameters that establish the scenarios of the neuronal responses. We have verified analytically the existence and stability of Hopf bifurcations. The memristive system can produce cascade of period doubling bifurcations for particular parameter regimes. Next, we investigate the emergence of multi-arm antispiral waves in the diffusively coupled system with proper analytical justification. We have also computed the group and phase velocities to discern the spiral and antispiral waves near the Hopf instability. A transition from target wave to multi-arm antispiral wave is observed in the diffusive system. Moreover, we use a random network architecture different from the diffusive network to study the dynamics of the coupled network for certain firing activities. It is observed that the network of heterogeneous desynchronized neurons with higher electrical couplings, can generate MMOs, MMBOs, and bursting for different external stimuli. However, the uncoupled systems cannot reveal such typical dynamics for particular parameters. Further, we introduce a reduced-order model to summarize the complete dynamics of the larger random network and report the findings.