Artículos de revistas
Metastable Periodic Patterns in Singularly Perturbed Delayed Equations
Fecha
2010Registro en:
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, v.22, n.2, p.203-252, 2010
1040-7294
10.1007/s10884-010-9158-1
Autor
GROTTA-RAGAZZO, C.
MALTA, Coraci Pereira
PAKDAMAN, K.
Institución
Resumen
We consider the scalar delayed differential equation epsilon(x) over dot(t) = -x(t) + f(x(t-1)), where epsilon > 0 and f verifies either df/dx > 0 or df/dx < 0 and some other conditions. We present theorems indicating that a generic initial condition with sign changes generates a solution with a transient time of order exp(c/epsilon), for some c > 0. We call it a metastable solution. During this transient a finite time span of the solution looks like that of a periodic function. It is remarkable that if df/dx > 0 then f must be odd or present some other very special symmetry in order to support metastable solutions, while this condition is absent in the case df/dx < 0. Explicit epsilon-asymptotics for the motion of zeroes of a solution and for the transient time regime are presented.