Application of normal forms to the Lorenz model in the subcritical region

Pade, Jochen; Rauh, Alexander; Tsarouhas, George

doi:10.1016/0167-2789(87)90059-5

“…Nevertheless, as rigorously proved under rather general conditions on ǫ, the normal form decouples into a low-dimensional dominant and a slaved [7] subsystem in the sense that stability of the dominant system induces stability of the remaining degrees of freedom. The theorem proved generalizes previous work [8,9].…”

Section: Introductionsupporting

confidence: 84%

Nonlinear stability analysis of plane poiseuille flow by normal forms

Rauh

¹

,

Zachrau

²

,

Zoller

³

1995

Physica D: Nonlinear Phenomena

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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“…The classical application deals with celestial mechanics [174,247], with the natural extension to problems concerning the appeaxance of periodic or chaotic behavior (see, for example, [187,198,216,267,325] for some recent contributions). Results very similar to those holding for the Hamiltonian case are also available for reversible systems [64,213,294,295].…”

Section: Birkhoff-gustavson Normal Formsmentioning

confidence: 99%

“…We mention here: [35,37,115,184,311,313] for applications concerning the physics of elementary particle accelerators, [36] for problems in magnetically confined plasmas and beam dynamics, [267] for applications to the Lorenz model, and [10] for a recent and relevant application to stochastic equations. Several other applications will be mentioned in the next chapters, being especially related to the case of Hamiltonian systems, both in classical and in quantum mechanics.…”

mentioning

confidence: 99%

Symmetry and Perturbation Theory in Nonlinear Dynamics

1999

Lecture Notes in Physics

78

0

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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“…original one. However, within the NFT we normally So we will briefly outline the above scheme here, neglect the~, and consider successively higher order while the reader should refer to the quoted works for approximate systems, which are formed by the first details [3]. For the sake of simplicity in the den-two terms on the r.h.s.…”

Section: Pmentioning

confidence: 99%

Normal form analysis of integrable Hamiltonian systems

Filho

¹

,

Andrade

²

1991

Physics Letters A

1

0

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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Application of normal forms to the Lorenz model in the subcritical region

Cited by 8 publications

References 24 publications

Nonlinear stability analysis of plane poiseuille flow by normal forms

Nonlinear stability analysis of plane poiseuille flow by normal forms

Symmetry and Perturbation Theory in Nonlinear Dynamics

Normal form analysis of integrable Hamiltonian systems

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