Chaos In A Homogeneous Model For Earthquakes

TL;DR

This paper explores the complex nonlinear dynamics of a homogeneous earthquake model, revealing chaotic behavior, bifurcations, and sensitivity to initial conditions, advancing understanding of earthquake system unpredictability.

Contribution

It demonstrates the presence of chaos and bifurcations in a simplified homogeneous earthquake model, highlighting the nonlinear and sensitive nature of earthquake dynamics.

Findings

Presence of periodic, quasiperiodic, and chaotic orbits

Identification of routes to chaos via intermittencies and bifurcations

Quantification of sensitivity through Liapunov exponents

Abstract

We investigate the nonlinear properties of a system introduced by Burridge and Knopoff to model the dynamics of earthquakes. We find that a two-block system in a completely homogeneous configuration presents a complex behavior characterized by the presence of periodic, quasiperiodic and chaotic orbits. We have found routes to chaos via two types of intermittencies and period doubling bifurcations. The sensitivity of the evolution to different initial conditions is quantified by calculating the largest Liapunov exponent. The dynamics of the model is governed by nondifferentiable flows.