Mechanisms of stochastic excitement in a nonlinear thermochemical model of autocatalysis

Understanding the mechanisms of oscillatory behavior is an important issue in modern nonlinear dynamics. We study stochastic excitation of complex oscillations in a nonlinear dynamic model of thermokinetics. A wide diversity of mono- and bi-stability regimes in the deterministic version of this model is demonstrated. For the model that takes into account multiplicative stochastic disturbances, underlying mechanisms of transformations of equilibrium modes into the large-amplitude spiking oscillatory regimes are clarified. We study in detail scenarios of stochastic excitement with the help of direct numerical simulations and analytical stochastic sensitivity technique. The work demonstrates the constructive capabilities of geometric analysis of the relative positions of separatrices and confidence ellipses.