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Two-dimensional nonlinear map characterized by tunable Lévy flights.

J A Méndez-Bermúdez1, Juliano A de Oliveira2, Edson D Leonel3

  • 1Instituto de Física, Benemérita Universidad Autónoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 7, 2014
PubMed
Summary
This summary is machine-generated.

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Researchers developed a generalized nonlinear map (Mα) to generate Lévy flights, crucial for understanding particle movement and creating new pseudorandom number generators. This map simulates complex particle trajectories in disordered systems.

Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Chaos theory

Background:

  • Point particles in rippled billiards exhibit Lévy flights.
  • Lévy flights are characterized by a specific power-law distribution.

Purpose of the Study:

  • To derive a generalized nonlinear map (Mα) capable of producing Lévy flights.
  • To identify conditions for global chaos onset in the Mα map.
  • To explore the application of the Mα map as a Lévy pseudorandom number generator.

Main Methods:

  • Derivation of a generalized two-dimensional nonlinear map (Mα).
  • Application of Chirikov's overlapping resonance criteria to determine chaos onset.
  • Computation of scattering properties in disordered wires to validate the map.

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Main Results:

  • The generalized map Mα successfully produces Lévy flights for 0 < α < 2.
  • Conditions for global chaos onset were identified as a function of map parameters.
  • The Mα map demonstrated applicability in simulating scattering properties of disordered wires.

Conclusions:

  • The Mα map serves as a tool for generating Lévy flights and understanding related phenomena.
  • The study establishes criteria for using the Mα map as a Lévy pseudorandom number generator.
  • The findings confirm the map's utility in modeling physical systems like disordered wires.