Analysis of multimodal stochastic oscillations in a biochemical reaction model

This paper studies the dynamics of the two-dimensional biochemical Goldbeter model under the influence of random disturbances. The model describes an enzymatic reaction with nonlinear recirculation of a product into a substrate. We investigate parametric zones where the system exhibits the phenomenon of bistability: the coexistence of two stable periodic regimes or the coexistence of a stable equilibrium and a stable limit cycle. The noise-induced transitions of stochastic trajectories between deterministic attractors resulting in multimodal oscillations are demonstrated via the direct numerical simulation. It is shown how the effect of noise on the system changes the frequency and amplitude characteristics of stochastic self-oscillations.