Paper Info
Title
Sparse Recovery And Dictionary Learning To Identify The Nonlinear Dynamical Systems: One Step Toward Finding Bifurcation Points In Real Systems
Abstract
Modeling real dynamical systems is an important challenge in many areas of science. Extracting governing equations of systems from their time-series is a possible solution for such a challenge. In this paper, we use the sparse recovery and dictionary learning to extract governing equations of a system with parametric basis functions. In this algorithm, the assumption of sparsity in the functions of dynamical equations is used. The proposed algorithm is applied to different types of discrete and continuous nonlinear dynamical systems to show the generalization ability of this method. On the other hand, transition from one dynamical regime to another is an important concept in studying real world complex systems like biological and climate systems. Lyapunov exponent is an early warning index. It can predict bifurcation points in dynamical systems. Computation of Lyapunov exponent is a major challenge in its application in real systems, since it needs long time data to be accurate. In this paper, we use the predicted governing equation to generate long time-series, which is needed for Lyapunov exponent calculation. So the proposed method can help us to predict bifurcation points by accurate calculation of Lyapunov exponents.
Year
DOI
Venue
2019
10.1142/S0218127419500305
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
Field
DocType
Sparse coding, dictionary learning, governing equation, bifurcation points
Applied mathematics,Dictionary learning,Control theory,Neural coding,Nonlinear dynamical systems,Dynamical systems theory,Governing equation,Real systems,Mathematics,Bifurcation
Journal
Volume
Issue
ISSN
29
3
0218-1274
Citations 
PageRank 
References 
0
0.34
0
Authors
4
Name
Order
Citations
PageRank
Fahimeh Nazarimehr1228.26
Aboozar Ghaffari2575.00
Sajad Jafari314010.65
Seyed Mohammad Reza Hashemi Golpayegani4978.72