Preprint
Bridging the Gap between Reactivity, Contraction and Finite-Time Lyapunov Exponents
ArXiv.org
Cornell University
10/30/2024
DOI: 10.48550/arxiv.2410.23435
Abstract
This paper investigates the concept of reactivity for a nonlinear
discrete-time system and generalizes this concept to the case of the
p-iteration system, p > 1. We introduce a definition of reactivity for
nonlinear discrete-time systems based on a general weighted norm. Stability
conditions of the first iteration system based on the reactivity of p-iteration
system, p > 1 are provided for both linear-time varying systems and nonlinear
maps. We provide examples of stability analysis of linear time-varying, and
synchronization of chaotic maps using reactivity. We discuss the connection
between reactivity and well-established stability criteria, contraction, and
finite-time Lyapunov exponents. For the case of a linearized system about a
given trajectory and the study of the local stability of the synchronous
solution for networks of coupled maps, the reactivity of the p-iteration system
coincides with the finite-time Lyapunov exponent, with this time being equal to
p. In the limit of infinite p, the reactivity becomes the maximum Lyapunov
exponent, which allows us to bridge the gap between the master stability
function approach and the contraction theory approach to study the stability of
the synchronous solution for networks.
Details
- Title: Subtitle
- Bridging the Gap between Reactivity, Contraction and Finite-Time Lyapunov Exponents
- Creators
- Amirhossein Nazerian - University of New MexicoFrancesco Sorrentino - University of New MexicoZahra Aminzare - University of Iowa
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- DOI
- 10.48550/arxiv.2410.23435
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 10/30/2024
- Academic Unit
- Iowa Neuroscience Institute; Mathematics
- Record Identifier
- 9984743399902771
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