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

Journal metrics

Journal metrics

  • IF value: 1.129 IF 1.129
  • IF 5-year value: 1.519 IF 5-year
    1.519
  • CiteScore value: 1.54 CiteScore
    1.54
  • SNIP value: 0.798 SNIP 0.798
  • SJR value: 0.610 SJR 0.610
  • IPP value: 1.41 IPP 1.41
  • h5-index value: 21 h5-index 21
  • Scimago H <br class='hide-on-tablet hide-on-mobile'>index value: 48 Scimago H
    index 48
Discussion papers
https://doi.org/10.5194/npg-2016-11
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
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

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 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.

Nitish Sinha and Arun K. Singh
Interactive discussion
Status: closed
Status: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version Supplement - Supplement
Interactive discussion
Status: closed
Status: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version Supplement - Supplement
Nitish Sinha and Arun K. Singh
Nitish Sinha and Arun K. Singh
Viewed  
Total article views: 722 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
468 205 49 722 38 57
  • HTML: 468
  • PDF: 205
  • XML: 49
  • Total: 722
  • BibTeX: 38
  • EndNote: 57
Views and downloads (calculated since 01 Feb 2016)
Cumulative views and downloads (calculated since 01 Feb 2016)
Cited  
Saved  
No saved metrics found.
Discussed  
No discussed metrics found.
Latest update: 23 Mar 2019
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...
Citation