Stochastic averaging near long heteroclinic orbits

Richard B. Sowers

doi:10.1142/S0219493707001974

Stochastic averaging near long heteroclinic orbits

Richard B. Sowers

Research output: Contribution to journal › Article › peer-review

Abstract

We refine some of the bounds of [10]. There, we considered the effect of diffusive perturbations on a two-dimensional ODE with a heteroclinic cycle. We constructed corrector functions for asymptotically "glueing" together behavior of periodic orbits in the boundary layer near the heteroclinic cycle. Here, we adapt the analysis of [10] to allow for "long" heteroclinic cycles.

Original language	English (US)
Pages (from-to)	187-228
Number of pages	42
Journal	Stochastics and Dynamics
Volume	7
Issue number	2
DOIs	https://doi.org/10.1142/S0219493707001974
State	Published - Jun 2007

Keywords

Glueing conditions
Perturbed test functions
Singular perturbations

ASJC Scopus subject areas

Modeling and Simulation

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10.1142/S0219493707001974

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abstract = "We refine some of the bounds of [10]. There, we considered the effect of diffusive perturbations on a two-dimensional ODE with a heteroclinic cycle. We constructed corrector functions for asymptotically {"}glueing{"} together behavior of periodic orbits in the boundary layer near the heteroclinic cycle. Here, we adapt the analysis of [10] to allow for {"}long{"} heteroclinic cycles.",

keywords = "Glueing conditions, Perturbed test functions, Singular perturbations",

author = "Sowers, \{Richard B.\}",

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AU - Sowers, Richard B.

N1 - This material is based upon work supported by the National Science Foundation under Grant Nos. 0305925 and 0604249.

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Y1 - 2007/6

N2 - We refine some of the bounds of [10]. There, we considered the effect of diffusive perturbations on a two-dimensional ODE with a heteroclinic cycle. We constructed corrector functions for asymptotically "glueing" together behavior of periodic orbits in the boundary layer near the heteroclinic cycle. Here, we adapt the analysis of [10] to allow for "long" heteroclinic cycles.

AB - We refine some of the bounds of [10]. There, we considered the effect of diffusive perturbations on a two-dimensional ODE with a heteroclinic cycle. We constructed corrector functions for asymptotically "glueing" together behavior of periodic orbits in the boundary layer near the heteroclinic cycle. Here, we adapt the analysis of [10] to allow for "long" heteroclinic cycles.

KW - Glueing conditions

KW - Perturbed test functions

KW - Singular perturbations

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UR - https://www.scopus.com/pages/publications/34447325894#tab=citedBy

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DO - 10.1142/S0219493707001974

M3 - Article

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JO - Stochastics and Dynamics

JF - Stochastics and Dynamics

IS - 2

ER -

Stochastic averaging near long heteroclinic orbits

Abstract

Keywords

ASJC Scopus subject areas

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