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Related Experiment Videos

Some new systems that generate a uniform stochastic web.

L. Y. Yu1, R. H. Parmenter

  • 1Department of Physics, University of Arizona, Tucson, Arizona 85721.

Chaos (Woodbury, N.Y.)
|October 1, 1992
PubMed
Summary

Periodically kicked Hamiltonian systems with 1.5 degrees of freedom generate infinite stochastic webs, even with non-sinusoidal kicks. These systems exhibit symmetric chaos patterns across their phase space.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Chaos Theory

Background:

  • Periodically kicked Hamiltonian systems are fundamental models in classical and quantum dynamics.
  • Understanding the phase space structure and chaotic behavior is crucial for predicting system evolution.
  • Previous studies often focused on sinusoidal perturbations, limiting the scope of investigated systems.

Purpose of the Study:

  • To investigate the generation of stochastic webs in periodically kicked Hamiltonian systems with 1.5 degrees of freedom.
  • To explore the influence of non-sinusoidal kick terms on web formation and chaotic dynamics.
  • To analyze the phase space structure and sensitive dependence on initial conditions.

Main Methods:

  • Analysis of Hamiltonian systems with 1.5 degrees of freedom subjected to periodic kicks.
  • Inclusion of non-sinusoidal functions (square wave, sawtooth) in the kick term.
  • Investigation of resonance conditions, specifically q=4.
  • Examination of sensitive dependence on initial conditions to characterize chaos.

Main Results:

  • Demonstration that various classes of periodically kicked Hamiltonian systems generate infinite, uniform stochastic webs.
  • Observation that the kick term does not need to be sinusoidal or a small perturbation.
  • Identification of different web structures, deviating from square lattices under specific resonance conditions (q=4).
  • Confirmation of remarkably symmetric chaos patterns throughout the entire phase space.

Conclusions:

  • Periodically kicked Hamiltonian systems with 1.5 degrees of freedom robustly generate stochastic webs, irrespective of the kick term's waveform.
  • Symmetric chaotic patterns persist even when the web structure deviates from a simple lattice.
  • These findings expand the understanding of chaos in dynamical systems and the universality of stochastic web formation.

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