Analysis of stochastic excitability in a simple kinetic model of glycolysis

In this paper, the Selkov model describing glycolytic oscillations of substrate and product is considered.We have obtained a parametric zone of equilibria where, depending on the initial data, two types of transients are observed. It is shown that in this zone the system is highly sensitive even to small random perturbations. We demonstrate and study the phenomenon of stochastic generation of large-amplitude oscillations in the equilibrium zone. In the study of probability distributions of random trajectories of the forced system, it is shown that this phenomenon is associated with a stochastic $P$-bifurcation. The deformations of the frequency characteristics are confirmed by spectral analysis. It is shown that in the regime of the stochastic excitation of stable equilibrium, the dominant frequency of the noise-induced spikes practically coincides with the frequency of the deterministic relaxation oscillations observed just after the Andronov–Hopf bifurcation.