Synchronous Patterns in an Ensemble of Two Excitatory Coupled Nonidentical Excitable $\phi$-Neurons

The purpose of this study is to investigate a simple model for the half-center oscillator (HCO), which consists of two nonidentical phase oscillators ($\phi$-neurons) with mutual chemical excitatory couplings. In the absence of couplings, each element is in an excitable state. Using one- and two-parameter bifurcation analysis, we determine regions of stability of various synchronous temporal patterns typical for HCO and describe in detail bifurcation transitions between them. The proposed simple HCO model allows one to reproduce the main effects observed in biologically plausible HCO models, and can be easily implemented in locomotor units in neuromorphic robotics.