{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:28:06Z","timestamp":1787232486533,"version":"3.56.0"},"reference-count":62,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>We introduce distributed axonal transmission speeds and a long\u2010range constant feedback loop into the standard neural field model. We analyze the stability of spatially homogeneous equilibrium solutions for general connectivity kernels. By studying reduced models based on the assumption of small delays, we determine the effects of the delays on the stability and bifurcations. We show in a reduced model that delayed excitatory feedback generally facilitates stationary bifurcations and Turing patterns, while suppressing the bifurcation of periodic solutions and traveling waves. The reverse conclusion holds for inhibitory feedback. In case of oscillatory bifurcations, the variance of the distributed propagation and feedback delays affects the frequency of periodic solutions and the phase speed of traveling waves. Moreover, we give a nonlinear analysis of traveling fronts and find that distributed transmission speeds can maximize the front speed.<\/jats:p>","DOI":"10.1137\/050629367","type":"journal-article","created":{"date-parts":[[2006,12,11]],"date-time":"2006-12-11T14:43:47Z","timestamp":1165848227000},"page":"670-698","source":"Crossref","is-referenced-by-count":88,"title":["Neural Fields with Distributed Transmission Speeds and Long\u2010Range Feedback Delays"],"prefix":"10.1137","volume":"5","author":[{"given":"Fatihcan M.","family":"Atay","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Axel","family":"Hutt","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,12,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00337259"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139903430884"},{"key":"R3","unstructured":"R. Bellman,\n                      Introduction to Matrix Analysis\n                      , 2nd ed., McGraw\u2010Hill, New York, 1970."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2001.1.233"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.2466\/pms.1998.86.3.851"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1142\/S0217979297001209"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1126\/science.283.5402.695"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1016\/S0079-6123(08)60363-5"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/s00422-005-0574-y"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(03)00002-2"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.94.148102"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1137\/040605953"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008843412952"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/0013-4694(80)90011-5"},{"key":"R15","unstructured":"P. Dayan and L. F. Abbott,\n                      Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems\n                      , MIT Press, Cambridge, MA, 2001."},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2004.833130"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1126\/science.252.5009.1177"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1007\/BF00336965"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.95.208107"},{"key":"R20","unstructured":"W. J. Freeman,\n                      Mass Action in the Nervous System\n                      , Academic Press, New York, 1975."},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127492000653"},{"key":"R22","unstructured":"M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, M. Booth, and F. Rossia,\n                      GNU Scientific Library Reference Manual\n                      , 2nd ed., Network Theory, Bristol, U.K., 2003."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.51.738"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1152\/jn.2001.85.3.1328"},{"key":"R25","doi-asserted-by":"crossref","unstructured":"H. Haken,\n                      Brain Dynamics\n                      , Springer, Berlin, 2002.","DOI":"10.1007\/978-3-540-46284-2"},{"key":"R26","doi-asserted-by":"crossref","unstructured":"H. K. Hartline and F. Ratliff,\n                      Inhibitory interaction in the retina of Limulus\n                      , in Handbook of Sensory Physiology, Springer\u2010Verlag, New York, 1971, Vol. VII\/2, pp. 381\u2013447.","DOI":"10.1007\/978-3-642-65340-7_11"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.70.052902"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2005.03.002"},{"key":"R29","doi-asserted-by":"crossref","unstructured":"A. Hutt and F. M. Atay,\n                      Spontaneous and evoked activity in extended neural populations with gamma\u2010distributed spatial interactions and transmission delay\n                      , Chaos Solitons Fractals, (2007), to appear.","DOI":"10.1016\/j.chaos.2005.10.091"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1088\/0954-898X\/14\/2\/310"},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1385\/NI:2:2:183"},{"key":"R32","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.77.960"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2004.53.2431"},{"key":"R34","doi-asserted-by":"publisher","DOI":"10.1162\/089976600300015277"},{"key":"R35","unstructured":"R. D. Katznelson,\n                      Normal modes of the brain: Neuroanatomic basis and a physiologic theoretical model\n                      , in Electric Fields of the Brain: The Neurophysics of EEG, P. Nunez, ed., Oxford University Press, New York, 1981, pp. 401\u2013442."},{"key":"R36","doi-asserted-by":"publisher","DOI":"10.1137\/040612890"},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1080\/09548980500533461"},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1137\/030600040"},{"key":"R39","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(78)90004-9"},{"key":"R40","doi-asserted-by":"publisher","DOI":"10.1111\/j.0013-9580.2003.12005.x"},{"key":"R41","doi-asserted-by":"crossref","unstructured":"J. Milton and P. Jung, eds.\n                      Epilepsy as a Dynamic Disease\n                      , Springer\u2010Verlag, New York, 2002.","DOI":"10.1007\/978-3-662-05048-4"},{"key":"R42","first-page":"495","volume":"38","author":"Morelli L. G.","year":"2004","journal-title":"Eur. Phys. J. B Condens. Matter Phys."},{"key":"R43","doi-asserted-by":"publisher","DOI":"10.1098\/rstb.2002.1172"},{"key":"R44","unstructured":"P. L. Nunez,\n                      Neocortical Dynamics and Human EEG Rhythms\n                      , Oxford University Press, New York, Oxford, 1995."},{"key":"R45","doi-asserted-by":"publisher","DOI":"10.1016\/j.brainresrev.2004.04.008"},{"key":"R46","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139900346453"},{"key":"R47","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.91.230601"},{"key":"R48","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.94.14.7621"},{"key":"R49","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.63.041909"},{"key":"R50","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.56.826"},{"key":"R51","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.68.021922"},{"key":"R52","doi-asserted-by":"publisher","DOI":"10.1038\/35086012"},{"key":"R53","doi-asserted-by":"publisher","DOI":"10.1016\/S0896-6273(00)80821-1"},{"key":"R54","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.ne.18.030195.003011"},{"key":"R55","doi-asserted-by":"publisher","DOI":"10.1080\/net.12.4.409.421"},{"key":"R56","unstructured":"M. Steriade, E. G. Jones, and R. R. Llinas,\n                      Thalamic Oscillations and Signalling\n                      , Wiley, New York, 1990."},{"key":"R57","doi-asserted-by":"publisher","DOI":"10.1126\/science.8235588"},{"key":"R58","doi-asserted-by":"crossref","unstructured":"V. V. Braitenberg and A. Sch\u00fcz,\n                      Anatomy of the Cortex\n                      , Springer, Berlin, 1991.","DOI":"10.1007\/978-3-662-02728-8"},{"key":"R59","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(72)86068-5"},{"key":"R60","doi-asserted-by":"publisher","DOI":"10.1007\/s004220050550"},{"key":"R61","doi-asserted-by":"publisher","DOI":"10.1088\/0954-898X\/3\/3\/006"},{"key":"R62","doi-asserted-by":"publisher","DOI":"10.57262\/die\/1356060624"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/050629367","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:58:14Z","timestamp":1787230694000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/050629367"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":62,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/050629367"],"URL":"https:\/\/doi.org\/10.1137\/050629367","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}