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Time-delayed map as a model for open fluid flow.

Frederick H. Willeboordse1

  • 1Institute of Physics,(a)) University of Tsukuba, Ibaraki 305, Japan.

Chaos (Woodbury, N.Y.)
|July 1, 1992
PubMed
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A time-delayed map with interrupted feedback can model open fluid flow. This chaotic element mapping provides insights into complex fluid dynamics simulations.

Area of Science:

  • Complex Systems
  • Fluid Dynamics
  • Nonlinear Dynamics

Background:

  • Coupled map lattices (CMLs) are used to model complex spatio-temporal phenomena.
  • Open fluid flow presents unique challenges due to boundary conditions and external influences.
  • Time-delayed feedback systems exhibit rich dynamical behaviors, including chaos.

Purpose of the Study:

  • To establish an exact mapping between a simplified time-delayed chaotic system and a CML model.
  • To demonstrate the applicability of this mapping for simulating open fluid flow.

Main Methods:

  • Analysis of a single chaotic element with periodically interrupted feedback.
  • Formulation of a coupled map lattice (CML) model representing open fluid flow.
  • Demonstration of the exact mathematical equivalence between the two models.

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Main Results:

  • The time-delayed map with interrupted feedback is shown to be exactly equivalent to a CML model.
  • This equivalence allows for the simulation of open fluid flow using a simpler, well-understood chaotic system.

Conclusions:

  • A novel connection is established between time-delayed systems and CMLs for fluid flow.
  • This finding offers a new theoretical framework for understanding and simulating open fluid dynamics.