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Resonance and Hybrid Structures02:16

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Resonance Raman Spectroscopy of Extreme Nanowires and Other 1D Systems
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Published on: April 28, 2016

Resonances within chaos.

G Gallavotti1, G Gentile, A Giuliani

  • 1Dipartimento di Fisica, Universita' di Roma La Sapienza, 00185 Roma, Italy.

Chaos (Woodbury, N.Y.)
|July 5, 2012
PubMed
Summary
This summary is machine-generated.

Simple chaotic systems with periodic forcing can create strange attractors. This study analytically examines this phenomenon in basic models, complementing numerical observations.

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Area of Science:

  • * Physics
  • * Applied Mathematics
  • * Nonlinear Dynamics

Background:

  • * Chaotic systems exhibit complex, unpredictable behavior.
  • * Periodic forcing introduces external regular influence on dynamic systems.
  • * Strange attractors represent complex, fractal structures in phase space.

Purpose of the Study:

  • * To analytically investigate the development of periodically visited strange attractors in chaotic systems.
  • * To explore simple models that exhibit this phenomenon.
  • * To bridge the gap between numerical simulation and analytical understanding.

Main Methods:

  • * Analytical study of simple chaotic models.
  • * Investigation of systems under periodic forcing.
  • * Examination of the formation and properties of attractors.

Main Results:

  • * Demonstrated the analytical tractability of periodically visited strange attractors in specific models.
  • * Confirmed the phenomenon observed in numerical simulations through analytical methods.
  • * Provided a detailed study of the attractor's behavior.

Conclusions:

  • * Periodically visited strange attractors in chaotic systems are analytically approachable.
  • * Simple models offer valuable insights into complex dynamical phenomena.
  • * Analytical methods can fully characterize this behavior, enhancing theoretical understanding.