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

Lihua Shen, Martin Ostoja-Starzewski, Emilio Porcu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)27-41
Number of pages15
JournalMathematics and Mechanics of Complex Systems
Issue number1
StatePublished - 2015


  • Fractal
  • Hurst effect
  • Random dynamical system
  • Stochastic ordinary differential equation

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Numerical Analysis
  • Computational Mathematics


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