Journal article · Preprint article
Singular limit analysis of a model for earthquake faulting
In this paper we consider the one dimensional spring-block model describing earthquake faulting. By using geometric singular perturbation theory and the blow-up method we provide a detailed description of the periodicity of the earthquake episodes. In particular, the limit cycles arise from a degenerate Hopf bifurcation whose degeneracy is due to an underlying Hamiltonian structure that leads to large amplitude oscillations.
We use a Poincar\'e compactification to study the system near infinity. At infinity the critical manifold loses hyperbolicity with an exponential rate. We use an adaptation of the blow-up method to recover the hyperbolicity. This enables the identification of a new attracting manifold that organises the dynamics at infinity.
This in turn leads to the formulation of a conjecture on the behaviour of the limit cycles as the time-scale separation increases. We provide the basic foundation for the proof of this conjecture and illustrate our findings with numerics.
Language: | English |
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Year: | 2017 |
Pages: | 2805-34 |
ISSN: | 13616544 and 09517715 |
Types: | Journal article and Preprint article |
DOI: | 10.1088/1361-6544/aa712e |
ORCIDs: | Bossolini, Elena , Brøns, Morten and Kristiansen, Kristian Uldall |
Blowup Earthquake dynamics Hamiltonian systems Poincaré compactification Rate and state friction Singular perturbation