Maximal temperature of safe combustion in case of an autocatalytic reaction

We consider the problem of thermal explosion of a gas mixture in the case of an autocatalytic combustion reaction in a homogeneous medium. We determine the maximal temperature on the trajectories located in the transition region between the slow combustion regime and the explosive one

A new type of travelling wave solutions

We study the existence of combustion waves for an autocatalytic reaction in the non-adiabatic case. Basing on the fact that the reaction system has canard solutions separating the slow combustion regime from the explosive one, we prove by applying the geometric theory of singularly perturbed differential equations the existence of a new type of travelling waves solutions, the so-called canard travelling waves

Black swans and canards in two predator – one prey model

In this paper, we show how canards can be easily caught in a class of 3D systems with an exact black swan (a slow invariant manifold of variable stability). We demonstrate this approach to a canard chase via the two predator – one prey model. It is shown that the technique described allows us to get various 3D oscillations by changing the shape of the trajectories of two 2D-projections of the original 3D system

A geometric approach to the modelling of critical phenomena for a spray combustion model

The paper is devoted to the modelling of the critical phenomena in multiscale combustion models. Such models are usually described by singularly perturbed systems of differential equations to reflect the significant distinction in characteristic relaxation times of different physicochemical processes. The paper proposes an approach for modelling of critical phenomena on the basis of the geometric asymptotic method of invariant manifolds. The critical phenomenon means as a sharp change in the dynamics of the process under consideration. As an illustration of this approach a dynamic model of fuel spray ignition and combustion is considered. The realizability conditions for the critical regime is obtained in the form of the asymptotic expression for the control parameter. The main feature of the critical regime is that during it the temperature of the combustible mixture can reach a high value within the framework of a safe process. It is shown that the critical regime plays the role of a watershed between the slow combustion regimes and the thermal explosion

Canards, cascades de canards et cygnes noirs

International audienceThe paper is devoted to the investigation of the slow integral manifolds of variable stability. The existence of non periodic canards, canard cascades and black swans is stated. The theoretical developments are illustrated by several examples.L'article est consacré à l'étude de variétés lentes intégrales de stabilité variable. L'existence de canards non périodiques, de cascades de canard et des cygnes noirs est établie. Les développements théoriques sont illustrés par plusieurs exemples