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Friction memory effect in complex dynamics of earthquake model

Authorized Users Only
2013
Authors
Kostić, Srdan
Franović, Igor
Todorović, Kristina
Vasović, Nebojša
Article (Published version)
Metadata
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Abstract
In present paper, an effect of delayed frictional healing on complex dynamics of simple model of earthquake nucleation is analyzed, following the commonly accepted assumption that frictional healing represents the main mechanism for fault restrengthening. The studied model represents a generalization of Burridge-Knopoff single-block model with Dieterich-Ruina's rate and state dependent friction law. The time-dependent character of the frictional healing process is modeled by introducing time delay tau in the friction term. Standard local bifurcation analysis of the obtained delay-differential equations demonstrates that the observed model exhibits Ruelle-Takens-Newhouse route to chaos. Domain in parameters space where the solutions are stable for all values of time delay is determined by applying the Rouch, theorem. The obtained results are corroborated by Fourier power spectra and largest Lyapunov exponents techniques. In contrast to previous research, the performed analysis reveals t...hat even the small perturbations of the control parameters could lead to deterministic chaos, and, thus, to instabilities and earthquakes. The obtained results further imply the necessity of taking into account this delayed character of frictional healing, which renders complex behavior of the model, already captured in the case of more than one block.

Keywords:
Spring-block model / State variable / Time delay / Quasiperiodicity / Deterministic chaos
Source:
Nonlinear Dynamics, 2013, 73, 3, 1933-1943
Publisher:
  • Springer, Dordrecht
Funding / projects:
  • Magmatism and geodynamics of the Balkan Peninsula from Mesozoic to present day: significance for the formation of metallic and non-metallic mineral deposits (RS-176016)

DOI: 10.1007/s11071-013-0914-8

ISSN: 0924-090X

WoS: 000322014200059

Scopus: 2-s2.0-84880917220
[ Google Scholar ]
18
16
URI
https://farfar.pharmacy.bg.ac.rs/handle/123456789/1972
Collections
  • Radovi istraživača / Researchers’ publications
Institution/Community
Pharmacy
TY  - JOUR
AU  - Kostić, Srdan
AU  - Franović, Igor
AU  - Todorović, Kristina
AU  - Vasović, Nebojša
PY  - 2013
UR  - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1972
AB  - In present paper, an effect of delayed frictional healing on complex dynamics of simple model of earthquake nucleation is analyzed, following the commonly accepted assumption that frictional healing represents the main mechanism for fault restrengthening. The studied model represents a generalization of Burridge-Knopoff single-block model with Dieterich-Ruina's rate and state dependent friction law. The time-dependent character of the frictional healing process is modeled by introducing time delay tau in the friction term. Standard local bifurcation analysis of the obtained delay-differential equations demonstrates that the observed model exhibits Ruelle-Takens-Newhouse route to chaos. Domain in parameters space where the solutions are stable for all values of time delay is determined by applying the Rouch, theorem. The obtained results are corroborated by Fourier power spectra and largest Lyapunov exponents techniques. In contrast to previous research, the performed analysis reveals that even the small perturbations of the control parameters could lead to deterministic chaos, and, thus, to instabilities and earthquakes. The obtained results further imply the necessity of taking into account this delayed character of frictional healing, which renders complex behavior of the model, already captured in the case of more than one block.
PB  - Springer, Dordrecht
T2  - Nonlinear Dynamics
T1  - Friction memory effect in complex dynamics of earthquake model
VL  - 73
IS  - 3
SP  - 1933
EP  - 1943
DO  - 10.1007/s11071-013-0914-8
ER  - 
@article{
author = "Kostić, Srdan and Franović, Igor and Todorović, Kristina and Vasović, Nebojša",
year = "2013",
abstract = "In present paper, an effect of delayed frictional healing on complex dynamics of simple model of earthquake nucleation is analyzed, following the commonly accepted assumption that frictional healing represents the main mechanism for fault restrengthening. The studied model represents a generalization of Burridge-Knopoff single-block model with Dieterich-Ruina's rate and state dependent friction law. The time-dependent character of the frictional healing process is modeled by introducing time delay tau in the friction term. Standard local bifurcation analysis of the obtained delay-differential equations demonstrates that the observed model exhibits Ruelle-Takens-Newhouse route to chaos. Domain in parameters space where the solutions are stable for all values of time delay is determined by applying the Rouch, theorem. The obtained results are corroborated by Fourier power spectra and largest Lyapunov exponents techniques. In contrast to previous research, the performed analysis reveals that even the small perturbations of the control parameters could lead to deterministic chaos, and, thus, to instabilities and earthquakes. The obtained results further imply the necessity of taking into account this delayed character of frictional healing, which renders complex behavior of the model, already captured in the case of more than one block.",
publisher = "Springer, Dordrecht",
journal = "Nonlinear Dynamics",
title = "Friction memory effect in complex dynamics of earthquake model",
volume = "73",
number = "3",
pages = "1933-1943",
doi = "10.1007/s11071-013-0914-8"
}
Kostić, S., Franović, I., Todorović, K.,& Vasović, N.. (2013). Friction memory effect in complex dynamics of earthquake model. in Nonlinear Dynamics
Springer, Dordrecht., 73(3), 1933-1943.
https://doi.org/10.1007/s11071-013-0914-8
Kostić S, Franović I, Todorović K, Vasović N. Friction memory effect in complex dynamics of earthquake model. in Nonlinear Dynamics. 2013;73(3):1933-1943.
doi:10.1007/s11071-013-0914-8 .
Kostić, Srdan, Franović, Igor, Todorović, Kristina, Vasović, Nebojša, "Friction memory effect in complex dynamics of earthquake model" in Nonlinear Dynamics, 73, no. 3 (2013):1933-1943,
https://doi.org/10.1007/s11071-013-0914-8 . .

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