Order parameter for bursting polyrhythms in multifunctional central pattern generators

We examine multistability of several coexisting bursting patterns in a central pattern generator network composed of three Hodgkin-Huxley type cells coupled reciprocally by inhibitory synapses. We establish that the control of switching between bursting polyrhythms and their bifurcations are determined by the temporal characteristics, such as the duty cycle, of networked interneurons and the coupling strength asymmetry. A computationally effective approach to the reduction of dynamics of the nine-dimensional network to two-dimensional Poincaré return mappings for phase lags between the interneurons is presented.