Distance between chaotic trajectories by fractal dimension concepts
Document Type
Presentation Abstract
Presentation Date
10-20-2014
Abstract
Several concepts of dimension have been developed to characterize properties of chaotic trajectories. To estimate parameters of chaotic dynamical systems a measure to quantify the likelihood function of chaotic variability (the 'distance' between different trajectories) is needed. We review problems encountered by previously used method and propose a method related to the correlation dimension concept. The major advantage of the new construct is its insensitivity with respect to varying initial values, to the choice of a solver, numeric tolerances, etc. A way to create the statistical likelihood for model parameters is presented, together with a sound framework for Markov chain Monte Carlo sampling. The methodology is illustrated using computational examples for the Lorenz~63 and Lorenz~95 systems.
Recommended Citation
Haario, Heikki, "Distance between chaotic trajectories by fractal dimension concepts" (2014). Colloquia of the Department of Mathematical Sciences. 464.
https://scholarworks.umt.edu/mathcolloquia/464
Additional Details
Monday, October 20, 2014 at 3:10 p.m. in Math 103
4:00 p.m. Refreshments in Math Lounge 109