Relaxation oscillations, pulses, and travelling waves in the diffusive Volterra delay-differential equation

López Bonilla, Luis and Liñán Martínez, Amable (1984). Relaxation oscillations, pulses, and travelling waves in the diffusive Volterra delay-differential equation. "Siam Journal on Applied Mathematics", v. 44 (n. 2); pp. 369-391. ISSN 0036-1399.

Description

Title: Relaxation oscillations, pulses, and travelling waves in the diffusive Volterra delay-differential equation
Author/s:
  • López Bonilla, Luis
  • Liñán Martínez, Amable
Item Type: Article
Título de Revista/Publicación: Siam Journal on Applied Mathematics
Date: April 1984
ISSN: 0036-1399
Volume: 44
Subjects:
Freetext Keywords: differential equations; diffusion; oscillations; wave equations; discrete delay; travelling waves; delay differential equation; diffusive Volterra equation; continuous delay; matched asymptotic expansions; general normalized kernels; homogeneous relaxation oscillations; pulses; periodic wavetrains; pacemakers; leading centers
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Motopropulsión y Termofluidodinámica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

The diffusive Volterra equation with discrete or continuous delay is studied in the limit of long delays using matched asymptotic expansions. In the case of continuous delay, the procedure was explicitly carried out for general normalized kernels of the form Sigma/sub n=p//sup N/ g/sub n/(t/sup n//T/sup n+1/)e/sup -t/T/, pges2, in the limit in which the strength of the delayed regulation is much greater than that of the instantaneous one, and also for g/sub n/=delta/sub n2/ and any strength ratio. Solutions include homogeneous relaxation oscillations and travelling waves such as pulses, periodic wavetrains, pacemakers and leading centers, so that the diffusive Volterra equation presents the main features of excitable media.

More information

Item ID: 796
DC Identifier: http://oa.upm.es/796/
OAI Identifier: oai:oa.upm.es:796
Official URL: http://link.aip.org/link/?SMM/44/369/1
Deposited by: Archivo Digital UPM
Deposited on: 23 Dec 2007
Last Modified: 20 Apr 2016 06:31
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