Mathematics & Physics 2016, 9(3), 269–278 УДК 512.54 Analysis of the Stochastic Excitement in a Model of Flow Reactor Irina A. Bashkirtseva∗ Polina M.Fominykh† Institute of Mathematics and Computer Science Ural Federal University Lenina, 51, Ekaterinburg, 620000 Russia Received 07.04.2016, received in revised form 17.05.2016, accepted 20.06.2016 A probabilistic mechanism of the stochastic excitement in a model of flow reactor is studied. <...> To analyze this phenomenon in regions of mono- and bistability the stochastic sensitivity function technique and the method of confidence ellipses are used. <...> Introduction Mathematical modeling and analysis of nonlinear dynamical systems in the presence of random perturbations attracts attention of researchers from various fields of science. <...> It is well known that noise not only blurs the attractors of deterministic models but it can also lead to qualitative changes in the stochastic dynamics due to nonlinearity of these models. <...> The interplay of nonlinearity and stochasticity results in such phenomena as noise-induced transitions [1, 2], stochastic resonance [3,4], noise-induced order [5], chaos [6] and stochastic excitability [7]. <...> Typically, the system is extremely sensitive to noise near bifurcation points. <...> An analysis of the effects of noise on the oscillatory systems near the soft and hard Hopf bifurcations attracted attention of many researchers (see, e.g., [8–12]). <...> Among the models of chemical kinetics, models of chemical flow reactor with ideal mixing [15] play an important practical role. <...> One of the models of chemical flow reactor is considered in this paper. <...> The phenomenon of stochastic excitability is demonstrated and analyzed for this model. <...> There are well developed analytical methods for deterministic models. <...> The analysis of the stochastic dynamics of nonlinear systems faces serious difficulties. <...> The direct use of this equation is very difficult even in two-dimensional case. <...> All rights reserved c – 269 – Irina A. Bashkirtseva, Polina M.Fominykh Analysis of the Stochastic Excitement in a Model . one of the most common methods of stochastic analysis is a direct numerical simulation of random trajectories and their subsequent statistical processing. <...> Then the use of approximations and asymptotics based on the method of quasipotential [16] and the stochastic sensitivity functions technique [17, 18] is very actual. <...> A brief description <...>