Journal article
Stochastic Logarithmic Lipschitz Constants: A Tool to Analyze Contractivity of Stochastic Differential Equations
IEEE control systems letters, Vol.6, pp.2311-2316
02/02/2022
DOI: 10.1109/LCSYS.2022.3148945
Abstract
We introduce the notion of stochastic logarithmic Lipschitz constants and use these constants to characterize stochastic contractivity of ItC4 stochastic differential equations (SDEs) with multiplicative noise. We find an upper bound for stochastic logarithmic Lipschitz constants based on known logarithmic norms (matrix measures) of the Jacobian of the drift and diffusion terms of the SDEs. We discuss noise-induced contractivity in SDEs and common noise-induced synchronization in network of SDEs and illustrate the theoretical results on a noisy Van der Pol oscillator. We show that a deterministic Van der Pol oscillator is not contractive, while, adding multiplicative noises makes the system stochastically contractive.
Details
- Title: Subtitle
- Stochastic Logarithmic Lipschitz Constants: A Tool to Analyze Contractivity of Stochastic Differential Equations
- Creators
- Zahra Aminzare - Department of Mathematics, University of Iowa, IA, USA. (e-mail: zahra-aminzare@uiowa.edu)
- Resource Type
- Journal article
- Publication Details
- IEEE control systems letters, Vol.6, pp.2311-2316
- DOI
- 10.1109/LCSYS.2022.3148945
- eISSN
- 2475-1456
- Publisher
- IEEE
- Grant note
- name: Simon Foundations’, award: 712522; DOI: 10.13039/100000001, name: NSF, award: IOS-2037828
- Language
- English
- Date published
- 02/02/2022
- Academic Unit
- Iowa Neuroscience Institute; Mathematics
- Record Identifier
- 9984215029602771
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