Chaotic motion of localized structures

A. J. Alvarez-Socorro, Marcel G. Clerc, Michel Ferré, and Edgar Knobloch
Phys. Rev. E 101, 042212 – Published 27 April 2020

Abstract

Mobility properties of spatially localized structures arising from chaotic but deterministic forcing of the bistable Swift-Hohenberg equation are studied and compared with the corresponding results when the chaotic forcing is replaced by white noise. Short structures are shown to possess greater mobility, resulting in larger root-mean-square speeds but shorter displacements than longer structures. Averaged over realizations, the displacement of the structure is ballistic at short times but diffusive at larger times. Similar results hold in two spatial dimensions. The effects of chaotic forcing on the stability of these structures is also quantified. Shorter structures are found to be more fragile than longer ones, and their stability region can be displaced outside the pinning region for constant forcing. Outside the stability region the deterministic fluctuations lead either to the destruction of the structure or to its gradual growth.

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  • Received 19 November 2019
  • Revised 12 January 2020
  • Accepted 23 March 2020

DOI:https://doi.org/10.1103/PhysRevE.101.042212

©2020 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsStatistical Physics & Thermodynamics

Authors & Affiliations

A. J. Alvarez-Socorro1,2, Marcel G. Clerc1, Michel Ferré1, and Edgar Knobloch3

  • 1Departamento de Física and Millennium Institute for Research in Optics, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
  • 2Laboratorio de Investigación, Desarrollo e Innovación, Zenta Group, Diagonal Oriente 5081, Ñuñoa, Santiago, Chile
  • 3Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA

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Issue

Vol. 101, Iss. 4 — April 2020

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