This article is cited in 2 papers

Mathematical Modelling

Flow curvature applied to modelling of critical phenomena

M. O. Balabaev

Samara National Research University, 34, Moskovskoye shosse, Samara, 443086, Russian Federation

Abstract: Modeling of critical phenomena is a very important problem, which has direct applied application in many branches of science and technology. In this paper we regard a modification of the low curvature method applied to construction of invariant manifolds of autonomous fast-slow dynamic systems. We compared a new method with original ones via finding duck-trajectories and their multidimensional analogues — surfaces with variable stability. Comparison was used a three-dimensional autocatalytic reaction model and a model of the burning problem.

Keywords: differential equations, fast-slow systems, invariant manifolds, singular perturbations, critical phenomena, duck-trajectories, various stability, flow curvature, autocatalytic reaction, burning problem.

UDC: 517.928

Received: 11.03.2019
Accepted: 20.03.2019

DOI: 10.18287/2541-7525-2019-25-2-92-99