the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Linear and Non-linear Stability Analysis of the Rate and State Friction Model with Three State Variables
Nitish Sinha
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.
Nitish Sinha and Arun K. Singh


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RC1: 'Referee report on this paper', Anonymous Referee #1, 29 Feb 2016
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AC1: 'Reply on comments by Referee-1', Arun Singh, 06 Mar 2016
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AC2: 'Reply on comments by Referee-1', Arun Singh, 06 Mar 2016
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AC1: 'Reply on comments by Referee-1', Arun Singh, 06 Mar 2016
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RC2: 'Interactive comment on “Linear and Non-linear Stability Analysis of the Rate and State Friction Model with Three State Variables” by N. Sinha and A. K. Singh', Anonymous Referee #2, 20 Apr 2016
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AC3: 'Rebuttal to RC2 and modified manuscript', Arun Singh, 15 May 2016
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AC3: 'Rebuttal to RC2 and modified manuscript', Arun Singh, 15 May 2016


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RC1: 'Referee report on this paper', Anonymous Referee #1, 29 Feb 2016
-
AC1: 'Reply on comments by Referee-1', Arun Singh, 06 Mar 2016
-
AC2: 'Reply on comments by Referee-1', Arun Singh, 06 Mar 2016
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AC1: 'Reply on comments by Referee-1', Arun Singh, 06 Mar 2016
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RC2: 'Interactive comment on “Linear and Non-linear Stability Analysis of the Rate and State Friction Model with Three State Variables” by N. Sinha and A. K. Singh', Anonymous Referee #2, 20 Apr 2016
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AC3: 'Rebuttal to RC2 and modified manuscript', Arun Singh, 15 May 2016
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AC3: 'Rebuttal to RC2 and modified manuscript', Arun Singh, 15 May 2016
Nitish Sinha and Arun K. Singh
Nitish Sinha and Arun K. Singh
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