Metastable Periodic Patterns in Singularly Perturbed Delayed Equations


Autoria(s): GROTTA-RAGAZZO, C.; MALTA, Coraci Pereira; PAKDAMAN, K.
Contribuinte(s)

UNIVERSIDADE DE SÃO PAULO

Data(s)

20/10/2012

20/10/2012

2010

Resumo

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.

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Identificador

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, v.22, n.2, p.203-252, 2010

1040-7294

http://producao.usp.br/handle/BDPI/30551

10.1007/s10884-010-9158-1

http://dx.doi.org/10.1007/s10884-010-9158-1

Idioma(s)

eng

Publicador

SPRINGER

Relação

Journal of Dynamics and Differential Equations

Direitos

restrictedAccess

Copyright SPRINGER

Palavras-Chave #Metastability #Delayed differential equation #Singular perturbation #Transition layer #DISCRETE LYAPUNOV FUNCTION #DIFFERENTIAL-EQUATIONS #FEEDBACK #DECOMPOSITION #DYNAMICS #SYSTEMS #Mathematics, Applied #Mathematics
Tipo

article

original article

publishedVersion