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
Received: 17 Jan 2016 – Accepted for review: 28 Jan 2016 – Discussion started: 01 Feb 2016
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.
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., doi:10.5194/npg-2016-11, 2016.