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Related Experiment Video

Updated: Mar 19, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
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Generic superweak chaos induced by Hall effect.

Moti Ben-Harush1, Itzhack Dana1

  • 1Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.

Physical Review. E
|June 15, 2016
PubMed
Summary

The kicked Hall system (KHS) demonstrates that electric and magnetic fields can suppress chaos. This leads to "superweak" chaos, where chaotic behavior is significantly reduced, offering a stabilizing effect.

Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Plasma Physics

Background:

  • Charged particles in electric and magnetic fields exhibit complex dynamics.
  • Weak chaos in periodically kicked systems is sensitive to initial conditions.
  • The Hall effect arises from the interaction of charged particles with perpendicular electric and magnetic fields.

Purpose of the Study:

  • To introduce and investigate the kicked Hall system (KHS).
  • To explore the phenomenon of superweak chaos (SWC) in the KHS.
  • To analyze the stabilizing effect of the Hall effect on chaotic dynamics.

Main Methods:

  • Theoretical study of charged particle dynamics.
  • Analysis of the kicked Hall system with periodic potentials.
  • Investigation of the weak-chaos and superweak-chaos regimes.

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Main Results:

  • The Hall effect suppresses weak chaos in the KHS, leading to superweak chaos (SWC).
  • SWC reduces the effective kicking strength from κ to κ².
  • Instability of periodic orbits decreases, and chaotic layers narrow under SWC.
  • Chaotic diffusion on stochastic webs is significantly slower in SWC compared to weak chaos.

Conclusions:

  • The Hall effect provides a stabilizing influence on chaotic dynamics in the KHS for small kicking strengths.
  • Superweak chaos in the KHS is a generic phenomenon under resonant conditions.
  • The KHS offers a two-dimensional analog to higher-dimensional Arnol'd webs.