Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction

The Zeldovich–Semenov model of the continuous stirred tank reactor with parametric random disturbances in temperature is considered. We study a phenomenon of noise-induced transformation of the equilibrium mode into the mixed-mode oscillatory stochastic regime with alternations between small and large amplitudes. In the parametric analysis of the stochastic excitement, we use the analytical method of confidence domains based on the stochastic sensitivity technique. Analyzing a mutual arrangement of the confidence ellipses and separatrices, we estimate the critical intensity of the noise that causes the excitation. The phenomena of stochastic P-bifurcations and coherence resonances are discovered and studied by probability density functions and the statistics of interspike intervals.

Noise-induced complex oscillatory dynamics in the Zeldovich-Semenov model of a continuous stirred tank reactor

Noise-induced variability of thermochemical processes in a continuous stirred tank reactor is studied on the basis of the Zeldovich-Semenov dynamical model. For the deterministic variant of this model, mono- and bistability parametric zones as well as local and global bifurcations are determined. Noise-induced transitions between coexisting attractors (equilibria and cycles) and stochastic excitement with spike oscillations are investigated by direct numerical simulation and the analytical approach based on the stochastic sensitivity technique. For the stochastic model, the phenomenon of coherence resonance is discovered and studied.