Abstract
Bifurcation theory deals with the asymptotic (long time) behaviour of systems of differential equations (continuous time) or dynamical systems (discrete time). Generally these evolution laws are non-linear and involve a few adjustable parameters (for instance temperature or boundary conditions in hydrodynamics) (1,2). For certain critical values of these parameters, the asymptotic behaviour of the solution changes suddenly and qualitatively: this phenomenum is a bifurcation. This can be the transition from a stationary state to a limit cycle or from a periodic behaviour to a more erratic behaviour.
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Derrida, B. (1980). Critical Properties of One Dimensional Mappings. In: Bardos, C., Bessis, D. (eds) Bifurcation Phenomena in Mathematical Physics and Related Topics. NATO Advanced Study Institutes Series, vol 54. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9004-3_8
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DOI: https://doi.org/10.1007/978-94-009-9004-3_8
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