Nonequilibrium potentials and their power-series expansions

T. Tél, R. Graham, G. Hu

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

The analytic properties of nonequilibrium potentials are studied in a class of two-variable models undergoing a bifurcation of codimension higher than 1. Several methods for the construction of nonequilibrium potentials are given. Cases are exhibited explicitly where a polynomial expansion does not exist due to logarithmic terms, even though the potential remains smooth. It is concluded (i) that the nonexistence of polynomial expansions near bifurcation points of higher order, recently reported by several authors, does not imply the nonexistence of a smooth potential, and (ii) that even in cases where the Hamilton-Jacobi equation has a particular solution in the form of a power series, that particular solution may still fail to represent the nonequilibrium potential by failing to satisfy the necessary boundary condition at the attractor.

Original languageEnglish
Pages (from-to)4065-4071
Number of pages7
JournalPhysical Review A
Volume40
Issue number7
DOIs
Publication statusPublished - 1989

Fingerprint

power series
series expansion
polynomials
Hamilton-Jacobi equation
expansion
boundary conditions

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Atomic and Molecular Physics, and Optics

Cite this

Nonequilibrium potentials and their power-series expansions. / Tél, T.; Graham, R.; Hu, G.

In: Physical Review A, Vol. 40, No. 7, 1989, p. 4065-4071.

Research output: Contribution to journalArticle

Tél, T. ; Graham, R. ; Hu, G. / Nonequilibrium potentials and their power-series expansions. In: Physical Review A. 1989 ; Vol. 40, No. 7. pp. 4065-4071.
@article{8bfafd2611404cfcb2666d9d73ab66d5,
title = "Nonequilibrium potentials and their power-series expansions",
abstract = "The analytic properties of nonequilibrium potentials are studied in a class of two-variable models undergoing a bifurcation of codimension higher than 1. Several methods for the construction of nonequilibrium potentials are given. Cases are exhibited explicitly where a polynomial expansion does not exist due to logarithmic terms, even though the potential remains smooth. It is concluded (i) that the nonexistence of polynomial expansions near bifurcation points of higher order, recently reported by several authors, does not imply the nonexistence of a smooth potential, and (ii) that even in cases where the Hamilton-Jacobi equation has a particular solution in the form of a power series, that particular solution may still fail to represent the nonequilibrium potential by failing to satisfy the necessary boundary condition at the attractor.",
author = "T. T{\'e}l and R. Graham and G. Hu",
year = "1989",
doi = "10.1103/PhysRevA.40.4065",
language = "English",
volume = "40",
pages = "4065--4071",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "7",

}

TY - JOUR

T1 - Nonequilibrium potentials and their power-series expansions

AU - Tél, T.

AU - Graham, R.

AU - Hu, G.

PY - 1989

Y1 - 1989

N2 - The analytic properties of nonequilibrium potentials are studied in a class of two-variable models undergoing a bifurcation of codimension higher than 1. Several methods for the construction of nonequilibrium potentials are given. Cases are exhibited explicitly where a polynomial expansion does not exist due to logarithmic terms, even though the potential remains smooth. It is concluded (i) that the nonexistence of polynomial expansions near bifurcation points of higher order, recently reported by several authors, does not imply the nonexistence of a smooth potential, and (ii) that even in cases where the Hamilton-Jacobi equation has a particular solution in the form of a power series, that particular solution may still fail to represent the nonequilibrium potential by failing to satisfy the necessary boundary condition at the attractor.

AB - The analytic properties of nonequilibrium potentials are studied in a class of two-variable models undergoing a bifurcation of codimension higher than 1. Several methods for the construction of nonequilibrium potentials are given. Cases are exhibited explicitly where a polynomial expansion does not exist due to logarithmic terms, even though the potential remains smooth. It is concluded (i) that the nonexistence of polynomial expansions near bifurcation points of higher order, recently reported by several authors, does not imply the nonexistence of a smooth potential, and (ii) that even in cases where the Hamilton-Jacobi equation has a particular solution in the form of a power series, that particular solution may still fail to represent the nonequilibrium potential by failing to satisfy the necessary boundary condition at the attractor.

UR - http://www.scopus.com/inward/record.url?scp=4243616890&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243616890&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.40.4065

DO - 10.1103/PhysRevA.40.4065

M3 - Article

AN - SCOPUS:4243616890

VL - 40

SP - 4065

EP - 4071

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 7

ER -