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Singular Singularly Perturbed Systems

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

Abstract

In this chapter we consider singularly perturbed differential systems whose degenerate equations have an isolated but not simple solution. In that case, the standard theory to establish a slow integral manifold near this solution does not work. Applying scaling transformations and using the technique of gauge functions we reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate the method by several examples from control theory and chemical kinetics.

Keywords

  • Differential System
  • Invariant Manifold
  • Integral Manifold
  • Invariance Equation
  • Linear Algebraic System

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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Fig. 5.1
Fig. 5.2

Notes

  1. 1.

    A stable matrix is one whose eigenvalues all have strictly negative real parts.

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Shchepakina, E., Sobolev, V., Mortell, M.P. (2014). Singular Singularly Perturbed Systems. In: Singular Perturbations. Lecture Notes in Mathematics, vol 2114. Springer, Cham. https://doi.org/10.1007/978-3-319-09570-7_5

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