title: Emergent oscillations in unidirectionally coupled overdamped bistable systems.
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 (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.
authors.affiliation: Space and Naval Warfare Systems Center, Code 2363, 53560 Hull Street, San Diego, California 92152-5001, USA. bulsara@spawar.navy.mil
authors.forename: Adi R
authors.initials: AR
authors.lastname: Bulsara
authors.forename: Visarath
authors.initials: V
authors.lastname: In
authors.forename: Andy
authors.initials: A
authors.lastname: Kho
authors.forename: Patrick
authors.initials: P
authors.lastname: Longhini
authors.forename: Antonio
authors.initials: A
authors.lastname: Palacios
authors.forename: Wouter-Jan
authors.initials: WJ
authors.lastname: Rappel
authors.forename: Juan
authors.initials: J
authors.lastname: Acebron
authors.forename: Salvatore
authors.initials: S
authors.lastname: Baglio
authors.forename: Bruno
authors.initials: B
authors.lastname: Ando