Wave fronts in inhomogeneous neural field models
Identifieur interne : 003B61 ( Main/Exploration ); précédent : 003B60; suivant : 003B62Wave fronts in inhomogeneous neural field models
Auteurs : H. Schmidt [Allemagne] ; A. Hutt [France] ; L. Schimansky-Geier [Allemagne]Source :
- Physica. D [ 0167-2789 ] ; 2009.
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Abstract
In this work we investigate the influence of inhomogeneities on wave front propagation in an excitatory neural field model describing synaptic activity in the absence of delays. This allows the derivation of the spatial (and hence temporal) behaviour of the front velocity under the assumption that the front is approximatively homogeneous in a very small time window. With this assumption we can also derive the spatiotemporal behaviour of the membrane potential analytically in the vicinity of the wave front. In addition to this we investigate stationary solutions such as standingwave fronts and localised activity (so-called bumps) to determine the existence condition of travelling and standing fronts. Numerical results are included to point out the accordance of theory and simulation.
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Hutt</name><affiliation wicri:level="3"><inist:fA14 i1="02"><s1>LORIA, 615 Rue dujardin Botanique</s1><s2>54506 Vandoeuvre-lés-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation></author><author><name sortKey="Schimansky Geier, L" sort="Schimansky Geier, L" uniqKey="Schimansky Geier L" first="L." last="Schimansky-Geier">L. Schimansky-Geier</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Institut für Physik, Humboldt Universität zu Berlin, Newtonstr. 15</s1><s2>12489 Berlin</s2><s3>DEU</s3><sZ>1 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>Allemagne</country><placeName><region type="land" nuts="3">Berlin</region><settlement type="city">Berlin</settlement></placeName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">09-0295855</idno><date when="2009">2009</date><idno type="stanalyst">PASCAL 09-0295855 INIST</idno><idno type="RBID">Pascal:09-0295855</idno><idno type="wicri:Area/PascalFrancis/Corpus">000265</idno><idno type="wicri:Area/PascalFrancis/Curation">000762</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000222</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000222</idno><idno type="wicri:doubleKey">0167-2789:2009:Schmidt H:wave:fronts:in</idno><idno type="wicri:Area/Main/Merge">003C56</idno><idno type="wicri:source">HAL</idno><idno type="RBID">Hal:inria-00401531</idno><idno type="url">https://hal.inria.fr/inria-00401531</idno><idno type="wicri:Area/Hal/Corpus">005336</idno><idno type="wicri:Area/Hal/Curation">005336</idno><idno type="wicri:Area/Hal/Checkpoint">002E49</idno><idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">002E49</idno><idno type="wicri:doubleKey">0167-2789:2009:Schmidt H:wave:fronts:in</idno><idno type="wicri:Area/Main/Merge">003821</idno><idno type="wicri:Area/Main/Curation">003B61</idno><idno type="wicri:Area/Main/Exploration">003B61</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Wave fronts in inhomogeneous neural field models</title><author><name sortKey="Schmidt, H" sort="Schmidt, H" uniqKey="Schmidt H" first="H." last="Schmidt">H. Schmidt</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Institut für Physik, Humboldt Universität zu Berlin, Newtonstr. 15</s1><s2>12489 Berlin</s2><s3>DEU</s3><sZ>1 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>Allemagne</country><placeName><region type="land" nuts="3">Berlin</region><settlement type="city">Berlin</settlement></placeName></affiliation></author><author><name sortKey="Hutt, A" sort="Hutt, A" uniqKey="Hutt A" first="A." last="Hutt">A. Hutt</name><affiliation wicri:level="3"><inist:fA14 i1="02"><s1>LORIA, 615 Rue dujardin Botanique</s1><s2>54506 Vandoeuvre-lés-Nancy</s2><s3>FRA</s3><sZ>2 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region><settlement type="city">Vandœuvre-lès-Nancy</settlement></placeName></affiliation></author><author><name sortKey="Schimansky Geier, L" sort="Schimansky Geier, L" uniqKey="Schimansky Geier L" first="L." last="Schimansky-Geier">L. Schimansky-Geier</name><affiliation wicri:level="3"><inist:fA14 i1="01"><s1>Institut für Physik, Humboldt Universität zu Berlin, Newtonstr. 15</s1><s2>12489 Berlin</s2><s3>DEU</s3><sZ>1 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>Allemagne</country><placeName><region type="land" nuts="3">Berlin</region><settlement type="city">Berlin</settlement></placeName></affiliation></author></analytic><series><title level="j" type="main">Physica. D</title><title level="j" type="abbreviated">Physica, D</title><idno type="ISSN">0167-2789</idno><imprint><date when="2009">2009</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Physica. D</title><title level="j" type="abbreviated">Physica, D</title><idno type="ISSN">0167-2789</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Existence condition</term><term>Membranes</term><term>Models</term><term>Non linear phenomenon</term><term>Steady state solution</term><term>Travelling waves</term><term>Wave front</term><term>Wave propagation</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Front onde</term><term>Modèle</term><term>Propagation onde</term><term>Membrane</term><term>Solution stationnaire</term><term>Condition existence</term><term>Onde progressive</term><term>Phénomène non linéaire</term></keywords><keywords scheme="mix" xml:lang="en"><term>Inhomogeneous neural fields</term><term>Stationary solutions</term><term>Travelling wave fronts</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In this work we investigate the influence of inhomogeneities on wave front propagation in an excitatory neural field model describing synaptic activity in the absence of delays. This allows the derivation of the spatial (and hence temporal) behaviour of the front velocity under the assumption that the front is approximatively homogeneous in a very small time window. With this assumption we can also derive the spatiotemporal behaviour of the membrane potential analytically in the vicinity of the wave front. In addition to this we investigate stationary solutions such as standingwave fronts and localised activity (so-called bumps) to determine the existence condition of travelling and standing fronts. Numerical results are included to point out the accordance of theory and simulation.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>France</li></country><region><li>Berlin</li><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Berlin</li><li>Vandœuvre-lès-Nancy</li></settlement></list><tree><country name="Allemagne"><region name="Berlin"><name sortKey="Schmidt, H" sort="Schmidt, H" uniqKey="Schmidt H" first="H." last="Schmidt">H. Schmidt</name></region><name sortKey="Schimansky Geier, L" sort="Schimansky Geier, L" uniqKey="Schimansky Geier L" first="L." last="Schimansky-Geier">L. Schimansky-Geier</name></country><country name="France"><region name="Grand Est"><name sortKey="Hutt, A" sort="Hutt, A" uniqKey="Hutt A" first="A." last="Hutt">A. Hutt</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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