Critical phenomena in a model of fuel's heating in a porous medium

Abstract

Abstract. The autoignition of flammable liquid in an inert porous medium are studied. In this paper we concentrated on the critical case which is concerned with the phenomenon of delayed loss of stability in the dynamical model. The realizability conditions for the critical regime are obtained. It is shown that critical regime is modelled by a canard − a trajectory of slow-fast system, which first move near the stable part of the slow invariant manifold, then move near the unstable part of it.Keywords: ignition, critical phenomenon, canard, invariant manifold, delayed loss of stability.Citation: Shchepakina E.A. Critical phenomena in a model of fuel's heating in a porous medium.

Calculation of critical conditions for the filtration combustion model

“…To find the critical value of the parameter , it is possible to use special asymptotic formulae [4,7,8]. That approach was used in [5][6][7]9] for system (1)-(3), in [10][11][12][13][14][15][16][17][18][19] for other laser and chemical systems, and in [20][21][22][23][24] for some biological problems. In the next section the main results concerning this approach obtained for system (1)- (3) are given.…”

Critical Cases in Slow/Fast Control Problems

“…Other critical cases were considered, for example, in [3,4,[13][14][15][16][17][18][19][20][21]. The critical case (i) is considered in Section 2 as applied to the high-gain control problem, the case (ii) is considered in Section 3 as applied to the manipulator control, the case (iii) is considered in Section 4 as applied to the partially cheap control problem.…”

Three Scenarios for Changing of Stability in the Dynamic Model of Nerve Conduction

“…The first case corresponds to the transition of one real eigenvalue of the linearized fast subsystem through zero when the slow variables are changed. This scenario for delaying of the loss of stability in the singularly perturbed systems is associated with the canards or duck-trajectories [6][7][8][9][10][11][12][13][14][15][16]. In the second case a pair of complex conjugate eigenvalues passes from the left complex half-plane to the right one [17][18][19].…”