Effective bifurcation analysis: A time-stepper-based approach

Olof Runborg; Constantinos Theodoropoulos; Ioannis G. Kevrekidis

doi:10.1088/0951-7715/15/2/314

Effective bifurcation analysis: A time-stepper-based approach

Olof Runborg, Constantinos Theodoropoulos, Ioannis G. Kevrekidis

Chemical & Biological Engineering

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65 Scopus citations

Abstract

We introduce a numerical approach to perform the effective (coarse-scale) bifurcation analysis of solutions of dissipative evolution equations with spatially varying coefficients. The advantage of this approach is that the 'coarse model' (the averaged, effective equation) need not be explicitly constructed. The method only uses a time-integrator code for the detailed problem and judicious choices of initial data and integration times; the bifurcation computations are based on the so-called recursive projection method (Shroff and Keller 1993 SIAM J. Numer. Anal. 30 1099-120).

Original language	English (US)
Pages (from-to)	491-511
Number of pages	21
Journal	Nonlinearity
Volume	15
Issue number	2
DOIs	https://doi.org/10.1088/0951-7715/15/2/314
State	Published - Mar 2002

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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abstract = "We introduce a numerical approach to perform the effective (coarse-scale) bifurcation analysis of solutions of dissipative evolution equations with spatially varying coefficients. The advantage of this approach is that the 'coarse model' (the averaged, effective equation) need not be explicitly constructed. The method only uses a time-integrator code for the detailed problem and judicious choices of initial data and integration times; the bifurcation computations are based on the so-called recursive projection method (Shroff and Keller 1993 SIAM J. Numer. Anal. 30 1099-120).",

author = "Olof Runborg and Constantinos Theodoropoulos and Kevrekidis, {Ioannis G.}",

year = "2002",

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T2 - A time-stepper-based approach

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AU - Theodoropoulos, Constantinos

AU - Kevrekidis, Ioannis G.

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Y1 - 2002/3

N2 - We introduce a numerical approach to perform the effective (coarse-scale) bifurcation analysis of solutions of dissipative evolution equations with spatially varying coefficients. The advantage of this approach is that the 'coarse model' (the averaged, effective equation) need not be explicitly constructed. The method only uses a time-integrator code for the detailed problem and judicious choices of initial data and integration times; the bifurcation computations are based on the so-called recursive projection method (Shroff and Keller 1993 SIAM J. Numer. Anal. 30 1099-120).

AB - We introduce a numerical approach to perform the effective (coarse-scale) bifurcation analysis of solutions of dissipative evolution equations with spatially varying coefficients. The advantage of this approach is that the 'coarse model' (the averaged, effective equation) need not be explicitly constructed. The method only uses a time-integrator code for the detailed problem and judicious choices of initial data and integration times; the bifurcation computations are based on the so-called recursive projection method (Shroff and Keller 1993 SIAM J. Numer. Anal. 30 1099-120).

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SP - 491

EP - 511

JO - Nonlinearity

JF - Nonlinearity

IS - 2

ER -

Effective bifurcation analysis: A time-stepper-based approach

Abstract

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