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Responses of first-order dynamical systems to Matérn, Cauchy, and Dagum excitations

Lookup NU author(s): Professor Emilio Porcu

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Abstract

The responses of dynamical systems under random forcings is a well-understood area of research. The main tool in this area, as it has evolved over a century, falls under the heading of stochastic differential equations. Most works in the literature are related to random forcings with a known parametric spectral density. This paper considers a new framework: the Cauchy and Dagum covariance functions indexing the random forcings do not have a closed form for the associated spectral density, while allowing decoupling of the fractal dimension and Hurst effect. On the basis of a first-order stochastic differential equation, we calculate the transient second-order characteristics of the response under these two covariances and make comparisons to responses under white, Ornstein–Uhlenbeck, and Matérn noises.

Publication metadata

Author(s): Shen L, Ostoja-Starzewski M, Porcu E

Publication type: Article

Publication status: Published

Journal: Mathematics and Mechanics of Complex Systems

Year: 2015

Volume: 3

Issue: 1

Pages: 27–41

Print publication date: 13/02/2015

Acceptance date: 17/11/2013

ISSN (print): 2326-7186

ISSN (electronic): 2325-3444

Publisher: International Research Center for the Mathematics and Mechanics of Complex Systems

URL: https://doi.org/10.2140/memocs.2015.3.27

DOI: 10.2140/memocs.2015.3.27

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