Deterministic nonperiodic flow. (English) Zbl 1417.37129

Summary: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space. For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
A simple system representing cellular convection is solved numerically. All of the solutions are found to be unstable, and almost all of them are nonperiodic.
The feasibility of very-long-range weather prediction is examined in the light of these results.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
86A10 Meteorology and atmospheric physics
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