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Palabras claves o descriptores: DIFFERENCE EQUATIONS (Comienzo)
2 registros cumplieron la condición especificada en la base de información BIBCYT. ()
Registro 1 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Sedaghat, H. ; Kent, C. M.
Título: Criteria for the Convergence, Oscillation, and Bistability of Pulse Circulation in a Ring of Excitable Media
Páginas/Colación: 573-590 p.
Url: Ir a http://siamdl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SMJMAP000066000002000573000001&idtype=cvips&gifs=Yeshttp://siamdl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SMJMAP000066000002000573000001&idtype=cvips&gifs=Yes
SIAM Journal on Applied Mathematics Vol. 66, no. 2 Nov. 2005/Jan. 2006
Información de existenciaInformación de existencia

Palabras Claves: Palabras: ASYMPTOTIC STABILITY ASYMPTOTIC STABILITY, Palabras: BISTABILITY BISTABILITY, Palabras: DIFFERENCE EQUATIONS DIFFERENCE EQUATIONS, Palabras: NONLINEAR NONLINEAR, Palabras: PERSISTENT OSCILLATIONS PERSISTENT OSCILLATIONS, Palabras: REENTRY REENTRY, Palabras: RESTITUTION RESTITUTION

Resumen
RESUMEN

 

RESUMEN

 

A discrete model based on a nonlinear difference equation (equivalent to a coupled map lattice of high dimension) is used to study the dynamics of a circulating pulse in a ring of excitable media, such as cardiac cells. Based on the global and local properties of monotonic restitution and dispersion curves, criteria are obtained for the asymptotic stability of the unique steady state (pulse circulating at constant frequency) as well as for nonconvergent oscillatory behavior of all nonequilibrium trajectories (pulse circulating at variable frequency). We also demonstrate that in certain cases the system is bistable, where an asymptotically stable equilibrium coexists with stable oscillatory solutions.

 

Registro 2 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Dong Kim, Sang ; V. Parter, Seymour
Título: Semicirculant Preconditioning of Elliptic Operators
Páginas/Colación: pp. 767 - 795
Url: Ir a http://epubs.siam.org/sam-bin/dbq/article/40300http://epubs.siam.org/sam-bin/dbq/article/40300
Siam Journal on Numerical Analysis Vol. 41, no. 2 April-May 2004
Información de existenciaInformación de existencia

Palabras Claves: Palabras: CONVECTION-DIFFUSION EQUATION CONVECTION-DIFFUSION EQUATION, Palabras: DIFFERENCE EQUATIONS DIFFERENCE EQUATIONS, Palabras: LIMITING OPERATOR LIMITING OPERATOR, Palabras: PRECONDITIONING PRECONDITIONING

Resumen
In this work we consider the semicirculant preconditioning of elliptic differential operators of the form Lu := - \epsilon \Delta u + au_x + bu_y + cu $$ in two cases: $0 < \epsilon \ll 1$ and $\epsilon \equiv 1$. The paper [Numer. Math., 81 (1998), pp. 211--249] provided extremely interesting and useful results in the first case. On the other hand, those appear to contradict basic results on preconditioning given in [SIAM J. Numer. Anal., 27 (1990), pp. 656--694]. We reobtain the results of [Numer. Math., 81 (1998), pp. 211--249] by a new approach which we believe to be more transparent. We also clarify the situation regarding the apparent contradiction with [SIAM J. Numer. Anal., 27 (1990), pp. 656--694]. Finally, we describe the distribution of the preconditioned eigenvalues in the uniformly elliptic case, $\epsilon \equiv 1$.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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