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Catastrophes and Bifurcations

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Second Course in Ordinary Differential Equations for Scientists and Engineers

Part of the book series: Universitext ((UTX))

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Abstract

In the previous chapter we discussed various methods to analyze the stability of the equilibrium states of a dynamical system when the values of the system parameters are known and fixed. The objective of catastrophe and bifurcation theory is to investigate what happens to the type, number, and stability of the equilibrium states as a result of a continuous change in the system parameters. In other words catastrophe theory is concerned with the “dynamical analysis” of the equilibrium states as a function of the system parameters as compared to the “static analysis” of these states which were performed in the last chapter.

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Bibliography

  1. J. Guckenheimer and P. Holmes — Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, 1983.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, 01609, USA

    Mayer Humi & William Miller

Authors
  1. Mayer Humi
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  2. William Miller
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© 1988 Springer-Verlag New York Inc.

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Humi, M., Miller, W. (1988). Catastrophes and Bifurcations. In: Second Course in Ordinary Differential Equations for Scientists and Engineers. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3832-4_10

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  • DOI: https://doi.org/10.1007/978-1-4612-3832-4_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96676-2

  • Online ISBN: 978-1-4612-3832-4

  • eBook Packages: Springer Book Archive

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