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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Preprints
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.

  01 Feb 2016

01 Feb 2016

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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 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

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Nitish Sinha and Arun K. Singh

Nitish Sinha and Arun K. Singh

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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...
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