Emergent oscillations in unidirectionally coupled overdamped bistable systems

Adi R. Bulsara, Visarath In, Andy Kho, Patrick Longhini, Antonio Palacios, Wouter-Jan Rappel, Juan Acebron, Salvatore Baglio, and Bruno Ando
Phys. Rev. E 70, 036103 – Published 3 September 2004

Abstract

It is well known that overdamped unforced dynamical systems do not oscillate. However, well-designed coupling schemes, together with the appropriate choice of initial conditions, can induce oscillations when a control parameter exceeds a threshold value. In a recent publication [Phys. Rev. E, 68, 045102(R) (2003)], we demonstrated this behavior in a specific prototype system, a soft-potential mean-field description of the dynamics in a hysteretic “single-domain” ferromagnetic sample. The previous analysis of this work showed that N (odd) unidirectionally coupled elements with cyclic boundary conditions would, in fact, oscillate when a control parameter—in this case the coupling strength—exceeded a critical value. These oscillations are now finding utility in the detection of very weak “target” signals, via their effect on the oscillation characteristics, e.g., the frequency and asymmetry of the oscillation wave forms. In this paper we explore the underlying dynamics of this system. Scaling laws that govern the oscillation frequency in the vicinity of the critical point, as well as the zero-crossing intervals in the presence of a symmetry-breaking target dc signal, are derived; these quantities are germane to signal detection and analysis.

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  • Received 12 February 2004

DOI:https://doi.org/10.1103/PhysRevE.70.036103

©2004 American Physical Society

Authors & Affiliations

Adi R. Bulsara1,*, Visarath In1,†, Andy Kho1,‡, Patrick Longhini2,§, Antonio Palacios2,∥, Wouter-Jan Rappel3,¶, Juan Acebron4,**, Salvatore Baglio5,††, and Bruno Ando5,‡‡

  • 1Space and Naval Warfare Systems Center, Code 2363, 53560 Hull Street, San Diego, California 92152-5001, USA
  • 2Nonlinear Dynamics Group, Department of Mathematics & Statistics, San Diego State University, San Diego, California 92182, USA
  • 3Physics Department, University of California at San Diego, La Jolla, California 92093, USA
  • 4Dipartimento di Ingegneria dell’ Informazione, Università di Padova, Via Gradenigo 6/B, 35131 Padova, Italy
  • 5Dipartimento di Ingegneria Elettrica Elettronica e dei Sistemi, Università degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italy

  • *Electronic address: bulsara@spawar.navy.mil
  • Electronic address: visarath@spawar.navy.mil
  • Electronic address: kho@spawar.navy.mil
  • §Electronic address: plonghini@netzero.net
  • Electronic address: palacios@euler.sdsu.edu
  • Electronic address: rappel@physics.ucsd.edu
  • **Electronic address: acebron@dei.unipd.it
  • ††Electronic address: salvatore.baglio@diees.unict.it
  • ‡‡Electronic address: bruno.ando@diees.unict.it

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Vol. 70, Iss. 3 — September 2004

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