| Autor: |
Elena Bossolini, Morten Brøns, Kristian Uldall Kristiansen |
| Předmět: |
|
| Zdroj: |
Nonlinearity; Jul2017, Vol. 30 Issue 7, p1-1, 1p |
| Abstrakt: |
In this paper we consider a 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, we show that 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 Poincaré 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 the conjecture. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
|
