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• W3101645996 abstract "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 illustrate our findings with numerics and suggest an outline of the proof of this conjecture." @default.
• W3101645996 created "2020-11-23" @default.
• W3101645996 creator A5012378349 @default.
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• W3101645996 date "2017-06-07" @default.
• W3101645996 modified "2023-10-18" @default.
• W3101645996 title "Singular limit analysis of a model for earthquake faulting" @default.
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• W3101645996 doi "https://doi.org/10.1088/1361-6544/aa712e" @default.
• W3101645996 hasPublicationYear "2017" @default.
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