Bounding Averages Rigorously Using Semidefinite Programming: Mean Moments of the Lorenz System

We describe methods for proving bounds on infinite-time averages in differential dynamical systems. The methods rely on the construction of nonnegative polynomials with certain properties, similarly to the way nonlinear stability can be proved using Lyapunov functions. Nonnegativity is enforced by r...

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Bibliographic Details
Published in:	Journal of nonlinear science Vol. 28; no. 2; pp. 621 - 651
Main Author:	Goluskin, David
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.04.2018 Springer Nature B.V
Subjects:	Analysis Classical Mechanics Construction methods Economic Theory/Quantitative Economics/Mathematical Methods Formulations Interval arithmetic Liapunov functions Lorenz equations Lorenz system Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Orbital stability Parameters Polynomials Semidefinite programming Stability analysis Theoretical Trajectory analysis Upper bounds
ISSN:	0938-8974, 1432-1467
Online Access:	Get full text
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