9 research outputs found
Scaling and Correlation Functions in a Model of a Two-dimensional Earthquake Fault
We study numerically a two-dimensional version of the Burrige-Knopoff model.
We calculate spatial and temporal correlation functions and compare their
behavior with the results found for the one-dimensional model. The
Gutenberg-Richter law is only obtained for special choices of parameters in the
relaxation function. We find that the distribution of the fractal dimension of
the slip zone exhibits two well-defined peaks coeersponding to intermediate
size and large events.Comment: 14 pages, 23 Postscript figure
Computation of Lyapunov functions for systems with multiple attractors
We present a novel method to compute Lyapunov functions for continuous-time systems with multiple local attractors. In the proposed method one first computes an outer approximation of the local attractors using a graphtheoretic approach. Then a candidate Lyapunov function is computed using a Massera-like construction adapted to multiple local attractors. In the final step this candidate Lyapunov function is interpolated over the simplices of a simplicial complex and, by checking certain inequalities at the vertices of the complex, we can identify the region in which the Lyapunov function is decreasing along system trajectories. The resulting Lyapunov function gives information on the qualitative behavior of the dynamics, including lower bounds on the basins of attraction of the individual local attractors. We develop the theory in detail and present numerical examples demonstrating the applicability of our method