Abstract
The paper shows how the repulsive invariant manifolds of multiscale dynamical systems are used for modeling the critical phenomena. A dynamical model of fuel spray ignition is considered to illustrate this approach.
This work was funded by RFBR and Samara Region (project 16-41-630529-p) and the Ministry of Education and Science of the Russian Federation under the Competitiveness Enhancement Program of Samara University (2013–2020).
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References
I. Goldfarb, V. Gol’dshtein, I. Shreiber, and A. Zinoviev, Liquid drop effects on self-ignition of combustible gas, Proceedings of the 26th Symposium (International) on Combustion (Pittsburgh: The Combustion Institute, 1996), pp. 1557–1563
E.F. Mishechenko, NKh Rozov, Differential equations with small parameters and relaxation oscillations (Plenum Press, New York, 1980)
E. Shchepakina and V. Sobolev, “Black swans and canards in laser and combustion models”, in Singular Perturbations and Hysteresis, ed by M. Mortell, R. O’Malley, A. Pokrovskii, V. Sobolev. SIAM 207–256 (2005)
E. Shchepakina, V. Sobolev, M.P. Mortell, Singular perturbations. Introduction to system order reduction methods with applications. Lect. Notes in Math. 2114, Cham: Springer (2014)
V.A. Sobolev, E.A. Shchepakina, Self-ignition of dusty media. Combust. Explos. Shock. Waves 29(3), 378–381 (1993)
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Shchepakina, E. (2019). Repulsive Invariant Manifolds in Modeling the Critical Phenomena. In: Korobeinikov, A., Caubergh, M., Lázaro, T., Sardanyés, J. (eds) Extended Abstracts Spring 2018. Trends in Mathematics(), vol 11. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-25261-8_17
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DOI: https://doi.org/10.1007/978-3-030-25261-8_17
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