Abstract
Numerical algorithms for determination of bifurcation points in steady State and periodic solutions are presented. Results of an evaluation of the limit points in a distributed parameter system where shooting method cannot be used are shown in the form of bifurcation diagram. Four direct iteration algorithms for an evaluation of complex (Hopf) bifurcation points in lumped parameter systems (ordinary differential equations) are described and applied to an example taken from the chemical reactor theory. An algorithm for determination of complex bifurcation points in distributed parameter systems (parabolic par-tial differential equations) is developed and results for a model of tubulär reactor with axial dispersion are presented.Two algorithms for evaluation of period doubling bifurcation points in periodic solutions of ordinary differential equations are suggested. Results of the application to a model of two inter-connected reaction cells are presented.
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Kubíček, M., Holodniok, M. (1984). Numerical Deterkination of Bifurcation Points in Steady State and Periodic Solutions — Numerical Algorithms and Examples. In: Küpper, T., Mittelmann, H.D., Weber, H. (eds) Numerical Methods for Bifurcation Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6256-1_17
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DOI: https://doi.org/10.1007/978-3-0348-6256-1_17
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