Journal cover Journal topic
Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

Journal metrics

  • IF value: 1.329 IF 1.329
  • IF 5-year<br/> value: 1.394 IF 5-year
    1.394
  • CiteScore<br/> value: 1.27 CiteScore
    1.27
  • SNIP value: 0.903 SNIP 0.903
  • SJR value: 0.709 SJR 0.709
  • IPP value: 1.455 IPP 1.455
  • h5-index value: 20 h5-index 20
https://doi.org/10.5194/npg-2016-11
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Research article
01 Feb 2016
Review status
This discussion paper is a preprint. It has been under review for the journal Nonlinear Processes in Geophysics (NPG). The revised manuscript was not accepted.
Linear and Non-linear Stability Analysis of the Rate and State Friction Model with Three State Variables
Nitish Sinha and Arun K. Singh Visves varaya National Institute of Technology, Nagpur-440010, INDIA
Abstract. In this article, we study linear and non-linear stability of the three state variables rate and state friction (3sRSF) model with spring-mass sliding system. Linear stability analysis shows that critical stiffness, at which dynamical behaviour of the sliding system changes, increases with number of state variables. The bifurcation diagram reveals that route of chaos is period doubling and this has also been confirmed with the Poincaré maps. The present system is hyperchaos since all Lyapunov exponents are positive. It is also established that the 3sRSF model is more chaotic than corresponding to the 2sRSF model. Finally, the implication of the present study is also discussed.

Citation: Sinha, N. and Singh, A. K.: Linear and Non-linear Stability Analysis of the Rate and State Friction Model with Three State Variables, Nonlin. Processes Geophys. Discuss., https://doi.org/10.5194/npg-2016-11, 2016.
Nitish Sinha and Arun K. Singh
Nitish Sinha and Arun K. Singh

Viewed

Total article views: 480 (including HTML, PDF, and XML)

HTML PDF XML Total BibTeX EndNote
330 128 22 480 18 27

Views and downloads (calculated since 01 Feb 2016)

Cumulative views and downloads (calculated since 01 Feb 2016)

Saved

Discussed

Latest update: 24 Nov 2017
Publications Copernicus
Download
Short summary
We have studied stability of the three state variables rate and state friction (3sRSF) model with spring-mass sliding system. Linear analysis shows that critical stiffness, at which dynamical behaviour of the sliding system changes, increases with number of state variables. The bifurcation diagram reveals that route of chaos is period doubling and this has also been confirmed with the Poincaré maps. The present system is hyperchaos since all Lyapunov exponents are positive.
We have studied stability of the three state variables rate and state friction (3sRSF) model...
Share