Inhibitory electromagnetic induction current induces enhancement instead of reduction of neural bursting activities

Abstract

Nonlinear dynamics play an important role in identifying complex behaviors, dynamical mechanisms, and physiological functions of the neural firing activities. In contrast to the common viewpoint that the inhibitory effect should induce the reduction of neural firing activities, the present paper presents a novel example that inhibitory effect mediated by the electromagnetic induction current can induce the enhancement of bursting activities, which is characterized by the increase of firing frequency and period-adding bifurcations of bursting patterns, i.e. more spikes appearing within a burst. With the fast/slow variable dissection method and bifurcation analysis of the fold/homoclinic bursting pattern of the Hindmarsh–Rose model, the dynamical mechanism of the enhanced bursting activities induced by inhibitory effect is acquired and is different from the one induced by excitatory effect. With increasing the inhibitory effect of induction current, more spikes appear in a burst due to that the burst becomes wider, which is induced by the left shift of the initial phase of the burst, i.e. the fold/saddle-node bifurcation point of equilibrium of the fast subsystem. However, with increasing the excitatory effect of the stimulation, the period of limit cycle/spiking of the fast subsystem becomes short, which leads to that the interspike interval within a burst becomes short and then the burst contains more spikes. Furthermore, the enhancement of bursting activities induced by the inhibitory and excitatory effects is verified in a digital circuit which is designed in the Digital Signal Processor environment of MATLAB system. The result provides a novel example of nonlinear phenomenon contrast to the traditional viewpoint of the inhibitory effect and implies that the inhibitory induction current may be used as a possible measure to modulate the firing frequency and bursting patterns.