Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs

Abstract

Abstract. Earthquake sequencing studies allow us to investigate empirical relationships among spatio-temporal parameters describing the complexity of earthquake properties. We have recently studied the relevance of Markov chain models to draw information from global earthquake catalogues. In these studies, we considered directed graphs as graph theoretic representations of the Markov chain model and analyzed their properties. Here, we look at earthquake sequencing itself as a directed graph. In general, earthquakes are occurrences resulting from significant stress interactions among faults. As a result, stress-field fluctuations evolve continuously. We propose that they are akin to the dynamics of the collective behavior of weakly coupled non-linear oscillators. Since mapping of global stress-field fluctuations in real time at all scales is an impossible task, we consider an earthquake zone as a proxy for a collection of weakly coupled oscillators, the dynamics of which would be appropriate for the ubiquitous Kuramoto model. In the present work, we apply the Kuramoto model with phase lag to the nonlinear dynamics on a directed graph of a sequence of earthquakes. For directed graphs with certain properties, the Kuramoto model yields synchronization, and inclusion of nonlocal effects evokes the occurrence of chimera states or the co-existence of synchronous and asynchronous behavior of oscillators. In this paper, we show how we build the directed graphs derived from global seismicity data. Then, we present conditions under which chimera states could occur and, subsequently, point out the role of the Kuramoto model in understanding the evolution of synchronous and asynchronous regions. We surmise that one implication of the emergence of chimera states will lead to investigation of the present and other mathematical models in detail to generate global chimera-state maps similar to global seismicity maps for earthquake forecasting studies.

Polaritonic network as a paradigm for dynamics of coupled oscillators

“…This is the Sakaguchi-Kuramoto model of coupled oscillators [54] with α representing a phase lag. Synchronisation and desynchronisation in this system has been extensively studied in the contexts as vastly different as a network of Wien-bridge oscillators in an experimental regime for which they can be approximated as phase oscillators [55], power grids consisting of many oscillating generators [56], and earthquake sequencing studies [57]. The phase lag appears as a result of synaptic organisations in neuroscience systems, time delays in sensor networks, or transfer conductances in power networks.…”

Exponential synchronization of the high-dimensional Kuramoto model with identical oscillators under digraphs

“…Kuramoto model is one of the most representative mathematical models of complex dynamical networks, which was first proposed by Yoshiki Kuramoto to describe and explain the synchronization phenomena in the real world [10]. Kuramoto model and its many variations have been applied to many fields such as neuro-science [3], power systems [5], chemical engineering [11], geophysics [22], and semiconductor lasers arrays [9]. The interconnecting network of the original Kuramoto model is a complete graph or the all-to-all topology.…”

Synchronization of quaternion‐valued coupled systems with time‐varying coupling via event‐triggered impulsive control

“…Remark Kuramoto models and their many variations have been applied widely, such as power systems, 38 neuro‐science, 39 geophysics, 40 and semiconductor lasers arrays 41 . However, to the best of authors' knowledge, few scholars take quaternion‐valued Kuramoto oscillators into account in previous work.…”