{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T17:42:38Z","timestamp":1775842958251,"version":"3.50.1"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2006,5]]},"abstract":"<jats:p> Dynamics of spiral waves in perturbed, e.g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. The forces are defined as a convolution of the perturbation with the spirals Response Functions, which are eigenfunctions of the adjoint linearized problem. In this paper we find numerically the Response Functions of a spiral wave solution in the classic excitable FitzHugh\u2013Nagumo model, and show that they are effectively localized in the vicinity of the spiral core. <\/jats:p>","DOI":"10.1142\/s0218127406015490","type":"journal-article","created":{"date-parts":[[2006,8,21]],"date-time":"2006-08-21T07:10:02Z","timestamp":1156144202000},"page":"1547-1555","source":"Crossref","is-referenced-by-count":30,"title":["LOCALIZATION OF RESPONSE FUNCTIONS OF SPIRAL WAVES IN THE FITZHUGH\u2013NAGUMO SYSTEM"],"prefix":"10.1142","volume":"16","author":[{"given":"I. V.","family":"BIKTASHEVA","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Liverpool, Liverpool L69 7ZL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. V.","family":"HOLDEN","sequence":"additional","affiliation":[{"name":"School of Biological Sciences, University of Leeds, Leeds LS2 9JT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V. N.","family":"BIKTASHEV","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1021\/jp002237n"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1099\/00221287-85-2-321"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1161\/01.RES.33.1.54"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/0960-0779(93)E0044-C"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127496001582"},{"key":"rf8","unstructured":"V. N.\u00a0Biktashev, Encyclopedia of Nonlinear Science, ed. 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