ABSTRACT
The transient fire growth in enclosed spaces is modelled using concepts of non linear dynamical systems theory and the theory of stochastic processes. The mathematical model, derived by a simplified thermodynamic approach to the problem, keeps into account two non linear effects on the burning rate of the fire: the radiation feedback from the hot layer to the fuel and the switch-over between fuel and ventilation control. The zone model used to derive the evolution of the temperature excess of the hot smoke layer is recast in the form of a gradient type dynamical system. A swallowtail catastrophe function is introduced to approximate the fire potential function and to define the boundaries of stable system behaviour. To perform a probabilistic analysis the temperature excess of the smoke layer is considered to be a stochastic variable the time evolution of which is modelled by a Langevin equation. The numerical solution of the corresponding Fokker-Planck equation allows to determine the probability density function of the stochastic process.
