Skip to Main content Skip to Navigation
Reports

Solitary waves in the excitable Burridge-Knopoff model

José Eduardo Morales Morales 1 Guillaume James 1, 2 Arnaud Tonnelier 1 
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann
Abstract : The Burridge-Knopoff model is a lattice differential equation describing a chain of blocks connected by springs and pulled over a surface. This model was originally introduced to investigate nonlinear effects arising in the dynamics of earthquake faults. One of the main ingredients of the model is a nonlinear velocity-dependent friction force between the blocks and the fixed surface. For some classes of non-monotonic friction forces, the system displays a large response to perturbations above a threshold, which is characteristic of excitable dynamics. Using extensive numerical simulations, we show that this response corresponds to the propagation of a solitary wave for a broad range of friction laws (smooth or nonsmooth) and parameter values. These solitary waves develop shock-like profiles at large coupling (a phenomenon connected with the existence of weak solutions in a formal continuum limit) and propagation failure occurs at low coupling. We introduce a simplified piecewise linear friction law (reminiscent of the McKean nonlinearity for excitable cells) which allows us to obtain analytical expression of solitary waves and study some of their qualitative properties, such as wavespeed and propagation failure. We propose a possible physical realization of this system as a chain of impulsively forced mechanical oscillators. In certain parameter regimes, non-monotonic friction forces can also give rise to bistability between the ground state and limit-cycle oscillations and allow for the propagation of fronts connecting these two stable states.
Document type :
Reports
Complete list of metadata

Cited literature [51 references]  Display  Hide  Download

https://hal.inria.fr/hal-01411897
Contributor : Arnaud Tonnelier Connect in order to contact the contributor
Submitted on : Wednesday, December 7, 2016 - 5:02:59 PM
Last modification on : Tuesday, April 26, 2022 - 8:48:01 AM
Long-term archiving on: : Tuesday, March 21, 2017 - 12:10:17 PM

File

RR-8996.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01411897, version 1

Citation

José Eduardo Morales Morales, Guillaume James, Arnaud Tonnelier. Solitary waves in the excitable Burridge-Knopoff model. [Research Report] RR-8996, INRIA Grenoble - Rhône-Alpes. 2016. ⟨hal-01411897⟩

Share

Metrics

Record views

169

Files downloads

230