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Type III intermittency without characteristic relation.

Ezequiel Del Rio1, Sergio Elaskar2

  • 1Department of Applied Physics, ETSI Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Cardenal Cisneros 3, 28040 Madrid, Spain.

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Summary
This summary is machine-generated.

Chaotic intermittency dynamics are re-examined. A non-uniform reinjection probability density (RPD) in 1D maps leads to ill-defined characteristic relations, challenging classical intermittency theory and experimental determination.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Statistical Physics

Background:

  • Chaotic intermittency involves transitions between laminar and chaotic states.
  • The reinjection probability density (RPD) governs transitions from chaotic to laminar dynamics.
  • Classical intermittency theory assumes a constant RPD, leading to specific characteristic relations.

Purpose of the Study:

  • To generalize intermittency theory for non-uniform RPDs observed in 1D maps.
  • To investigate the experimental observability of RPD and characteristic relations.
  • To extend analytical results for maps with generalized RPDs.

Main Methods:

  • Analytical extension of previous results for 1D maps with non-uniform RPDs.
  • Analysis of how RPD shape changes with map parameters.
  • Development of analytical expressions for RPD and characteristic relations.

Main Results:

  • A non-uniform RPD's shape significantly varies with small parameter changes, making it ill-defined.
  • Classical characteristic relations are not well-defined or experimentally determinable for these maps.
  • A novel characteristic relation was found to converge to a constant value.

Conclusions:

  • The classical intermittency framework is insufficient for certain 1D maps with non-uniform RPDs.
  • Experimental determination of characteristic relations may be challenging due to RPD variability.
  • The study introduces a new characteristic relation and validates findings with numerical simulations.