Quasi-periodic Henon-like attractors in the Lorenz-84 climate model with seasonal forcing

HW Broer; R Vitolo; C Simo

Quasi-periodic Henon-like attractors in the Lorenz-84 climate model with seasonal forcing

HW Broer^*, R Vitolo, C Simo

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

A class of strange attractors is described, occurring in a low-dimensional model of general atmospheric circulation. The differential equations of the system are subject to periodic forcing, where the period is one year - as suggested by Lorenz in 1984. The dynamics of the system is described in terms of a Poincare map, computed by numerical means. It is conjectured that certain strange attractors observed in the Poincare map are of quasi-periodic Henon-like type, i.e., they coincide with the closure of the unstable manifold of a quasi-periodic invariant circle of saddle type. A route leading to the formation of such strange attractors is presented. It involves a finite number of quasi-periodic period doubling bifurcations, followed by the destruction of an invariant circle due to homoclinic tangency.

Original language	English
Title of host publication	EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS
Editors	F Dumortier, H Broer, J Mawhin, A Vanderbauwhede, SV Lunel
Place of Publication	SINGAPORE
Publisher	World Scientific Publishing
Pages	601-606
Number of pages	6
ISBN (Print)	981-256-169-2
Publication status	Published - 2005
Event	International Conference on Differential Equations - , Belgium Duration: 1-Jan-2005 → 1-Jan-2005

Other

Other	International Conference on Differential Equations
Country/Territory	Belgium
Period	01/01/2005 → 01/01/2005

Keywords

STRANGE ATTRACTORS

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@inproceedings{c4c601a488844c398602a397e3673b1e,

title = "Quasi-periodic Henon-like attractors in the Lorenz-84 climate model with seasonal forcing",

abstract = "A class of strange attractors is described, occurring in a low-dimensional model of general atmospheric circulation. The differential equations of the system are subject to periodic forcing, where the period is one year - as suggested by Lorenz in 1984. The dynamics of the system is described in terms of a Poincare map, computed by numerical means. It is conjectured that certain strange attractors observed in the Poincare map are of quasi-periodic Henon-like type, i.e., they coincide with the closure of the unstable manifold of a quasi-periodic invariant circle of saddle type. A route leading to the formation of such strange attractors is presented. It involves a finite number of quasi-periodic period doubling bifurcations, followed by the destruction of an invariant circle due to homoclinic tangency.",

keywords = "STRANGE ATTRACTORS",

author = "HW Broer and R Vitolo and C Simo",

year = "2005",

language = "English",

isbn = "981-256-169-2",

pages = "601--606",

editor = "F Dumortier and H Broer and J Mawhin and A Vanderbauwhede and SV Lunel",

booktitle = "EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS",

publisher = "World Scientific Publishing",

note = "International Conference on Differential Equations ; Conference date: 01-01-2005 Through 01-01-2005",

}

Broer, HW, Vitolo, R & Simo, C 2005, Quasi-periodic Henon-like attractors in the Lorenz-84 climate model with seasonal forcing. in F Dumortier, H Broer, J Mawhin, A Vanderbauwhede & SV Lunel (eds), EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS. World Scientific Publishing, SINGAPORE, pp. 601-606, International Conference on Differential Equations, Belgium, 01/01/2005.

Quasi-periodic Henon-like attractors in the Lorenz-84 climate model with seasonal forcing. / Broer, HW; Vitolo, R; Simo, C.
EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS. ed. / F Dumortier; H Broer; J Mawhin; A Vanderbauwhede; SV Lunel. SINGAPORE: World Scientific Publishing, 2005. p. 601-606.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Quasi-periodic Henon-like attractors in the Lorenz-84 climate model with seasonal forcing

AU - Broer, HW

AU - Vitolo, R

AU - Simo, C

PY - 2005

Y1 - 2005

N2 - A class of strange attractors is described, occurring in a low-dimensional model of general atmospheric circulation. The differential equations of the system are subject to periodic forcing, where the period is one year - as suggested by Lorenz in 1984. The dynamics of the system is described in terms of a Poincare map, computed by numerical means. It is conjectured that certain strange attractors observed in the Poincare map are of quasi-periodic Henon-like type, i.e., they coincide with the closure of the unstable manifold of a quasi-periodic invariant circle of saddle type. A route leading to the formation of such strange attractors is presented. It involves a finite number of quasi-periodic period doubling bifurcations, followed by the destruction of an invariant circle due to homoclinic tangency.

AB - A class of strange attractors is described, occurring in a low-dimensional model of general atmospheric circulation. The differential equations of the system are subject to periodic forcing, where the period is one year - as suggested by Lorenz in 1984. The dynamics of the system is described in terms of a Poincare map, computed by numerical means. It is conjectured that certain strange attractors observed in the Poincare map are of quasi-periodic Henon-like type, i.e., they coincide with the closure of the unstable manifold of a quasi-periodic invariant circle of saddle type. A route leading to the formation of such strange attractors is presented. It involves a finite number of quasi-periodic period doubling bifurcations, followed by the destruction of an invariant circle due to homoclinic tangency.

KW - STRANGE ATTRACTORS

M3 - Conference contribution

SN - 981-256-169-2

SP - 601

EP - 606

BT - EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS

A2 - Dumortier, F

A2 - Broer, H

A2 - Mawhin, J

A2 - Vanderbauwhede, A

A2 - Lunel, SV

PB - World Scientific Publishing

CY - SINGAPORE

T2 - International Conference on Differential Equations

Y2 - 1 January 2005 through 1 January 2005

ER -

Quasi-periodic Henon-like attractors in the Lorenz-84 climate model with seasonal forcing

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