Abstract
Chaos is not restricted to systems without any spatial extension: it in fact occurs commonly in spatially extended dynamical systems that are most typically described by nonlinear partial differential equations (PDEs). If the patterns generated by such a system change randomly in time, we speak of spatiotemporal chaos, a kind of temporally chaotic pattern-forming process. If, in addition, the patterns are also spatially irregular, there is fully developed spatiotemporal chaos. In principle, the phase-space dimension of a spatially extended dynamical system is infinite. However, in practice, when a spatial discretization scheme is used to solve the PDE, or when measurements are made in a physical experiment with finite spatial resolution, the effective dimension of the phase space is not infinite but still high.
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Notes
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Plane Poiseuille flows are linearly unstable, but the critical Reynolds number is much above the value at which turbulence transition occurs [217].
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© 2011 Springer Science+Business Media, LLC
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Lai, YC., Tél, T. (2011). Transient Chaos in Spatially Extended Systems. In: Transient Chaos. Applied Mathematical Sciences, vol 173. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6987-3_9
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DOI: https://doi.org/10.1007/978-1-4419-6987-3_9
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