A Boolean delay equation model of colliding cascades. Part I: Multiple seismic regimes

摘要

We consider a prominent feature of hierarchical nonlinear ("complex'') systems: persistent recurrence of abrupt overall changes, called here "critical transitions.'' Motivated by the earthquake prediction problem, we formulate a model that uses heuristic constraints taken from the dynamics of seismicity. Our conclusions, though, may apply to hierarchical systems that arise in other areas. We use the Boolean delay equation (BDE) framework to model the dynamics of colliding cascades, in which a direct cascade of loading interacts with an inverse cascade of failures. The elementary interactions of elements in the system are replaced by their integral effect, represented by the delayed switching of an element's state. The present paper is the first of two on the BDE approach to modeling seismicity. Its major results are the following: (i) A model that implements the approach. (ii) Simulating three basic types of seismic regime. (iii) A study of regime switching in a parameter space of the loading and healing rates. The second paper focuses on the earthquake prediction problem. [References: 66]