The effect of noise on a bistable regime in the dynamical model of locomotor rhythm

The ultimate goal of this research is finding phenomenological parameters for correct estimation of the state of the nervous system controlling locomotor rhythm. As a first step we propose to use parameters of a dynamical system that models central pattern generator (CPG) of locomotor rhythm. Such a system gives qualitative description of dynamics of involuntary walking movements evoked by muscle vibration, in particular, bistability of regimes of forward and backward stepping and chaotic switchings between them. We demonstrate that, under certain conditions, such a system gives not only qualitative but also quantitative description, which enables one to use its parameters for correct estimation of the state of nervous system. Specific analysis reduces to considering the interaction of two identical Van der Pol-Duffing oscillators with nonlinear coupling the action of which qualitatively resembles combined action of excitatory and inhibitory couplings typical of neural networks. Within the framework of this model, switching of the regimes of forward and backward stepping observed in experiments is analogous to type-I intermittency (following the Pomeau-Manneville classification) but modified to the conditions of symmetry of the system under consideration. It was found that introduction of weak noise does not lead to a change of qualitative details of the oscillograms describing spontaneous transitions between the regimes. At the same time, the scalings of durations of these regimes between transitions change notably from the dependence typical of type-I intermittency to the dependence corresponding to on-off intermittency