Friction memory effect in complex dynamics of earthquake model
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 chaosSource:
Nonlinear Dynamics, 2013, 73, 3, 1933-1943Publisher:
- Springer, Dordrecht
Funding / projects:
DOI: 10.1007/s11071-013-0914-8
ISSN: 0924-090X
WoS: 000322014200059
Scopus: 2-s2.0-84880917220
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Institution/Community
PharmacyTY - 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 . .