dc.contributor.author | Vateman, Michael D. | |
dc.contributor.author | Van Vleck, Erik S. | |
dc.date.accessioned | 2015-03-30T21:35:37Z | |
dc.date.available | 2015-03-30T21:35:37Z | |
dc.date.issued | 2006-07-31 | |
dc.identifier.citation | Batemen, Michael D. & Van Vleck, Erik."Traveling Wave Solutions to a Coupled System of Spatially Discrete Nagumo Equations." (2006) SIAM J. Appl. Math., 66(3), 945–976. (32 pages). http://dx.doi.org/10.1137/050624352. | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/17248 | |
dc.description | This is the published version, also available here: http://dx.doi.org/10.1137/050624352. | en_US |
dc.description.abstract | We consider a coupled system of discrete Nagumo equations and derive traveling wave solutions to this system using McKean's caricature of the cubic. A certain form of this system is used to model ephaptic coupling between pairs of nerve axons. We study the difference $g(c)=a_1-a_2$ between the detuning parameters $a_i$ that is required to make both waves move at the same speed c. Of particular interest is the effect of a coupling parameter $\alpha$ and an "alignment" parameter A on the function g. Numerical investigation indicates that for fixed A, there exists a time delay value $\beta$ that results in $g=0$, and for large enough wave speeds, multiple such $\beta$ values exist. Also, numerical results indicate that the perturbation of $\alpha$ away from zero will yield additional solutions with positive wave speed when $A={1\over 2}$. We employ both analytical and numerical results to demonstrate our claims. | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.subject | discrete Nagumo equations | en_US |
dc.subject | ephaptic coupling | en_US |
dc.subject | traveling waves | en_US |
dc.title | Traveling Wave Solutions to a Coupled System of Spatially Discrete Nagumo Equations | en_US |
dc.type | Article | |
kusw.kuauthor | Van Vleck, Erik | |
kusw.kudepartment | Mathematics | en_US |
dc.identifier.doi | 10.1137/050624352 | |
kusw.oaversion | Scholarly/refereed, publisher version | |
kusw.oapolicy | This item meets KU Open Access policy criteria. | |
dc.rights.accessrights | openAccess | |