Geodesic
Flow curvature applied to modelling of critical phenomena
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 25 (2019) no. 2, pp. 92-99

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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, critical phenomena, duck-trajectories, various stability, flow curvature, burning problem.
Mots-clés : singular perturbations, autocatalytic reaction 
@article{VSGU_2019_25_2_a5,
     author = {M. O. Balabaev},
     title = {Flow curvature applied to modelling of critical phenomena},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {92--99},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2019_25_2_a5/}
}
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M. O. Balabaev. Flow curvature applied to modelling of critical phenomena. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 25 (2019) no. 2, pp. 92-99. http://geodesic.mathdoc.fr/item/VSGU_2019_25_2_a5/