Friction memory effect in complex dynamics of earthquake model

Kostić, Srđan; Franović, Igor; Todorović, Kristina; Vasović, Nebojša

doi:10.1007/s11071-013-0914-8

Cited by 24 publications

(16 citation statements)

References 33 publications

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“…Nevertheless, the high-frequent transients, presumably originating from the nearby earthquakes, further induce a transition to quasiperiodic-like motion, which is recognized as a third, precursory creep regime that typically occurs just before the seismic motion commences. This effect is analogous to the dynamics of the spring-slider model with time delay, where the Ruelle-Takens-Newhouse route to chaos28 may be found.…”

Section: Discussionmentioning

confidence: 56%

Triggered dynamics in a model of different fault creep regimes

Kostić

Franović

Perc

et al. 2014

Sci Rep

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The study is focused on the effect of transient external force induced by a passing seismic wave on fault motion in different creep regimes. Displacement along the fault is represented by the movement of a spring-block model, whereby the uniform and oscillatory motion correspond to the fault dynamics in post-seismic and inter-seismic creep regime, respectively. The effect of the external force is introduced as a change of block acceleration in the form of a sine wave scaled by an exponential pulse. Model dynamics is examined for variable parameters of the induced acceleration changes in reference to periodic oscillations of the unperturbed system above the supercritical Hopf bifurcation curve. The analysis indicates the occurrence of weak irregular oscillations if external force acts in the post-seismic creep regime. When fault motion is exposed to external force in the inter-seismic creep regime, one finds the transition to quasiperiodic- or chaos-like motion, which we attribute to the precursory creep regime and seismic motion, respectively. If the triggered acceleration changes are of longer duration, a reverse transition from inter-seismic to post-seismic creep regime is detected on a larger time scale.

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Section: Discussionmentioning

confidence: 56%

Triggered dynamics in a model of different fault creep regimes

Kostić

Franović

Perc

et al. 2014

Sci Rep

Self Cite

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“…However, Kostić et al (2013) have found chaotic behavior for small values of by introducing a time delay in the friction term. They have found two types of Hopf bifurcation depending on the variation of the time delay.…”

Section: Type Of Hopf Bifurcationmentioning

confidence: 99%

An upper limit for slow-earthquake zones: self-oscillatory behavior through the Hopf bifurcation mechanism from a spring-block model under lubricated surfaces

Castellanos-Rodríguez¹,

Campos-Cantón²,

Barboza-Gudiño³

et al. 2017

Nonlin. Processes Geophys.

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The complex oscillatory behavior of a springblock model is analyzed via the Hopf bifurcation mechanism. The mathematical spring-block model includes Dieterich-Ruina's friction law and Stribeck's effect. The existence of self-sustained oscillations in the transition zone -where slow earthquakes are generated within the frictionally unstable region -is determined. An upper limit for this region is proposed as a function of seismic parameters and frictional coefficients which are concerned with presence of fluids in the system. The importance of the characteristic length scale L, the implications of fluids, and the effects of external perturbations in the complex dynamic oscillatory behavior, as well as in the stationary solution, are take into consideration.

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“…Since then, abundant spring-block models were studied by excellent numerical simulations and statistical methods [8][9][10]. Time delay is introduced in one-block system transforming the system into infinite-dimensional, which makes it possible for the occurrence of deterministic chaos [11]. When it comes to periodic parameter perturbations, Kostić et al showed that minor perturbation to the parameters such as the oscillation amplitudes and the angular frequencies are sufficient to change the original behavior, leading to the onset of chaos [12].…”

Section: Introductionmentioning

confidence: 99%

Complex Dynamical Behaviors in a Spring‐Block Model with Periodic Perturbation

Chen

Ren

2019

Complexity

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A generalization of a Burridge-Knopoff spring-block model is investigated to illustrate the dynamics of transform faults. The model can undergo Hopf bifurcation and fold bifurcation of limit cycles. Considering the cyclical nature of the spring stiffness, the model with periodic perturbation is further explored via a continuation technique and numerical bifurcation analysis. It is shown that the periodic perturbation induces abundant dynamics, the existence, the switch, and the coexistence of multiple attractors including periodic solutions with various periods, quasiperiodic solutions, chaotic solutions through torus destruction, or cascade of period doublings. Throughout the results obtained, one can see that the system manifests complex dynamical behaviors such as chaos, self-organized criticality, and the transition of dynamical behaviors when it comes to periodic perturbations. Even very small variation of a parameter can result in radical changes of the dynamics, which provides a new insight into the fault dynamics.

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Friction memory effect in complex dynamics of earthquake model

Cited by 24 publications

References 33 publications

Triggered dynamics in a model of different fault creep regimes

Triggered dynamics in a model of different fault creep regimes

An upper limit for slow-earthquake zones: self-oscillatory behavior through the Hopf bifurcation mechanism from a spring-block model under lubricated surfaces

Complex Dynamical Behaviors in a Spring‐Block Model with Periodic Perturbation

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