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  • Letter

Origin of jumping oscillons in an excitable reaction-diffusion system

Edgar Knobloch1,*, Hannes Uecker2,†, and Arik Yochelis3,4,‡

  • 1Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
  • 2Institut für Mathematik, Universität Oldenburg, D26111 Oldenburg, Germany
  • 3Department of Solar Energy and Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, Midreshet Ben-Gurion 8499000, Israel
  • 4Department of Physics, Ben-Gurion University of the Negev, Be'er Sheva 8410501, Israel

  • *knobloch@berkeley.edu
  • †hannes.uecker@uni-oldenburg.de
  • ‡yochelis@bgu.ac.il
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Phys. Rev. E 104, L062201 – Published 8 December, 2021

DOI: https://doi.org/10.1103/PhysRevE.104.L062201

Abstract

Oscillons, i.e., immobile spatially localized but temporally oscillating structures, are the subject of intense study since their discovery in Faraday wave experiments. However, oscillons can also disappear and reappear at a shifted spatial location, becoming jumping oscillons (JOs). We explain here the origin of this behavior in a three-variable reaction-diffusion system via numerical continuation and bifurcation theory, and show that JOs are created via a modulational instability of excitable traveling pulses (TPs). We also reveal the presence of bound states of JOs and TPs and patches of such states (including jumping periodic patterns) and determine their stability. This rich multiplicity of spatiotemporal states lends itself to information and storage handling.

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Phys. Rev. E 104, L062201– Published 8 December, 2021
  • Received 19 July 2021
  • Accepted 23 November 2021
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