Black swan and curvature in an autocatalator model

Balabaev, M.O.

doi:10.1016/j.proeng.2017.09.614

Cited by 4 publications

(1 citation statement)

References 17 publications

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“…Фактически, такие поверхности целиком состоят из траекторий-уток, каждая из которых моделирует критическое, но при этом безопасное протекание некоторого процесса. Подобный подход к моделированию критических явлений был впервые применен в работе [8], а затем многократно использован в работах [9][10][11].…”

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Modeling Critical Phenomena in a Generalized Van Der Pol Model

Balabaev¹

2020

Izvestiya of SSC RAS

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named after Academician S.P. Korolyov In the framework of this paper we consider the fl ow curvature method applying to modeling critical phenomena in one of the three-timescale fast-slow autonomous dynamical systems. The article considers a model that is a generalization of the classical Van der Pol model. The approximations of an invariant manifold and a two-dimensional analogue of a duck trajectory (a black swan) are constructed.

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Section: предварительные сведенияunclassified

Modeling Critical Phenomena in a Generalized Van Der Pol Model

Balabaev¹

2020

Izvestiya of SSC RAS

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Flow curvature in a self-coupled FitzHugh-Nagumo model

Balabaev

2018

J. Phys.: Conf. Ser.

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Invariant manifold of variable stability in the Koper model

Balabaev

2019

J. Phys.: Conf. Ser.

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The Koper model is a vector field that was developed to study electrochemical oscillations arising in diffusion processes. In the framework of this paper, we consider the Koper model of chemical reactors. It is a three-dimensional autonomous slow-fast system with a folded node and a supercritical singular Hopf bifurcation. The aim is to construct the expansion of invariant manifold with variable stability and corresponding gluing function using the flow curvature method. We show that Koper model has sufficiently smooth invariant surface, called black swan. Computer simulation and computer algebra methods are used for the quantitative analysis of the model.

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Black swan and curvature in an autocatalator model

Cited by 4 publications

References 17 publications

Modeling Critical Phenomena in a Generalized Van Der Pol Model

Modeling Critical Phenomena in a Generalized Van Der Pol Model

Flow curvature in a self-coupled FitzHugh-Nagumo model

Invariant manifold of variable stability in the Koper model

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