Stochastic model for a wavelike exothermal reaction in condensed heterogeneous systems

The relationship between the stochastic and deterministic approaches to the description of the dynamic behavior for a nonlinear reacting system is studied. A self-propagating exothermal reaction in a heterogeneous medium has been chosen as an example. A stochastic model for this phenomenon is developed. The system is composed of cells characterized by temperature and degree of conversion, their transformation probability being dependent on temperature. Computer simulation showed that stochasticity reveals itself in the generation of disturbances that are absent in the deterministic model. For a well-developed steady-state regime, the distributions of the mean temperature and degree of conversion are close to those given by the deterministic model. Under the conditions of planar-wave-front instability, the stochastic model possesses a mechanism for spontaneous transfer to a stable regime from arbitrary initial conditions (temperature distribution, etc.) due to origination, propagation, and disintegration of disturbances. Such behavior agrees with experimental data and is not predicted by the deterministic model.