|
Organizers |
Propagation Failure of Traveling Fronts in Discrete Inhomogeneous Media
by
Brian Moore
University of Central Florida
Coauthors: Erik Van Vleck, University of Kansas,
and
Tony Humphries, McGill University
A crude model for electrical conduction in the nervous system is the spatially discrete Nagumo equation. Employing a piecewise linear approximation of the nonlinearity, one can derive exact solutions of this system such that a portion of the medium for conduction is deteriorated, characteristic of diseases that affect the nervous system. Using Jacobi operator theory, wave-like solutions are constructed for a problem with essentially arbitrary inhomogeneous discrete diffusion, and these solutions directly correspond to monotone traveling wave solutions in the case of homogeneous diffusion. A thorough study of the steady state solutions provides necessary and sufficient conditions for traveling waves to fail to propagate due to inhomogeneities in the medium.
Date received: March 31, 2009
Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayt-09.