Complex rhythm and synchronization of half-center oscillators under electromagnetic induction

Half-center oscillators are typical small circuits that are crucial for understanding CPG. The complex rhythms of CPG are closely related to certain diseases, such as epilepsy. This paper considered the influence of electromagnetic induction on the discharge mode of the half-center oscillators. First, we analyzed the response of individual firing neuron rhythms to electromagnetic induction when the slow-variable parameters vary. We also discussed the changes in the dynamic bifurcation structure when the intensity of electromagnetic induction varies. Furthermore, we determined the effects of mutually inhibitory and self-inhibitory synaptic parameters on the firing rhythm of the half-center oscillators. The different responses induced by electromagnetic induction interventions, showed that mutually inhibitory synapses modulate the firing rhythm weakly and self-inhibition synapses have a significant impact on firing rhythm. Finally, with the change of synaptic parameter values, the combined effects of autapse and mutually inhibitory synapses on the discharge rhythm of half-center oscillators were analyzed in symmetric and asymmetric autapse modes. It was found that the synchronous state of the half-center oscillators had a more robust electromagnetic induction response than the asynchronous state.