Emergence of spiral and antispiral patterns and its CGLE analysis in leech-heart interneuron model with electromagnetic induction

Abstract

Neurons can exhibit various rhythmic activities such as bursting, spiking, and quiescent states when exposed to external input current stimulus. In this paper, a model of medicinal leech's heart (LH) interneuron is considered to describe the dynamics of neurons with a varied range of electrical activities. The crucial insights into the model's dynamics are explored in three different parameter regimes: phasic spiking, regular spiking, and bursting, based upon the codimension-one bifurcation of the model by considering VK2shift as a bifurcation parameter. The spatiotemporal dynamics of the model are explored by allowing 1D and 2D diffusion in the membrane voltage. The 1D diffusive system produces irregular bursting dynamics for the intermediate value of diffusion coefficients, whereas, at higher values, it shows synchronized oscillations. In the presence of 2D diffusion, the emergence of different types of spiral patterns is observed in the system. Furthermore, the system is extended by incorporating electromagnetic induction in the membrane voltage to explore the effect of induction on the various dynamics of neural model. By varying its intensities, the membrane voltage in the extended model produces a variety of discharge modes, such as periodic spiking, fast-spiking, resting, and spike-adding phenomena. In addition, the emergence of anti-spiral patterns in the extended model near subcritical Hopf bifurcation is analytically verified using the complex Ginzburg-Landau equation (CGLE). These findings demonstrate that the firing patterns vary based on the control parameters, and these variations contribute to our understanding of how the brain system transmits and processes the signals.