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, 44 (2). pp. 369-391. ISSN 0036-1399
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| Item Type: | Article | ||||||
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| Title: | Relaxation oscillations, pulses, and travelling waves in the diffusive Volterra delay-differential equation | ||||||
| Journal/Publication Title: | Siam Journal on Applied Mathematics | ||||||
| Date: | April 1984 | ||||||
| Volume: | 44 | ||||||
| Number: | 2 | ||||||
| Department: | Motopropulsión and thermofluidynamic | ||||||
| Faculty: | E.T.S.I. Aeronautical (UPM) | ||||||
| Creative Commons licenses: | Recognition - No derivative works - No commercial | ||||||
| Item ID: | 796 | ||||||
| Subjects: | Mathematics |
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Official URL: http://link.aip.org/link/?SMM/44/369/1
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.
| Item Type: | Article |
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| Uncontrolled 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 |
| Subjects: | Mathematics |
| Código ID: | 796 |
| Depositado Por: | Archivo Digital UPM |
| Depositado el: | 23 Dec 2007 |
| Last Modified: | 14 Apr 2011 11:43 |
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