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Canards and Black Swans

Part of the Lecture Notes in Mathematics book series (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.

Keywords

  • Invariant Manifold
  • Integral Manifold
  • Critical Regime
  • Invariance Equation
  • Jump Point

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.

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

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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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