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Canards and Black Swans

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Singular Perturbations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2114))

Abstract

The chapter is devoted to the investigation of the relationship between slow integral manifolds of singularly perturbed differential equations and critical phenomena in chemical kinetics. We consider different problems e.g., laser models, classical combustion models and gas combustion in a dust-laden medium models, 3-D autocatalator model, using the techniques of canards and black swans. The existence of canard cascades is stated for the van der Pol model and models of the Lotka-Volterra type. The language of singular perturbations seems to apply to all critical phenomena even in the most disparate chemical systems.

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Notes

  1. 1.

    “An absurd story circulated as a hoax”, see Shorter Oxford English Dictionary.

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Authors and Affiliations

  1. Samara State Aerospace University, Samara, Russia

    Elena Shchepakina & Vladimir Sobolev

  2. University College Cork, Cork, Ireland

    Michael P. Mortell

Authors
  1. Elena Shchepakina
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  2. Vladimir Sobolev
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  3. Michael P. Mortell
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Shchepakina, E., Sobolev, V., Mortell, M.P. (2014). Canards and Black Swans. In: Singular Perturbations. Lecture Notes in Mathematics, vol 2114. Springer, Cham. https://doi.org/10.1007/978-3-319-09570-7_8

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