Status: this preprint was under review for the journal NPG but the revision was not accepted.
Linear and Non-linear Stability Analysis of the Rate and State Friction Model with Three State Variables
Nitish Sinhaand Arun K. Singh
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.
Received: 17 Jan 2016 – Discussion started: 01 Feb 2016
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.
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...
- Printer-friendly version
- Supplement