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

• 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

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...