Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2015-09-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | http://www.nonlin-processes-geophys.net/22/499/2015/npg-22-499-2015.pdf |
| _version_ | 1811339043762339840 |
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| author | K. Vasudevan M. Cavers A. Ware |
| author_facet | K. Vasudevan M. Cavers A. Ware |
| author_sort | K. Vasudevan |
| collection | DOAJ |
| description | 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 non-linear dynamics on a directed graph of a sequence of
earthquakes. For directed graphs with certain properties, the Kuramoto model
yields synchronization, and inclusion of non-local 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. |
| first_indexed | 2024-04-13T18:19:22Z |
| format | Article |
| id | doaj.art-091ef8da042a4fe7aa4131dbaba90473 |
| institution | Directory Open Access Journal |
| issn | 1023-5809 1607-7946 |
| language | English |
| last_indexed | 2024-04-13T18:19:22Z |
| publishDate | 2015-09-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Nonlinear Processes in Geophysics |
| spelling | doaj.art-091ef8da042a4fe7aa4131dbaba904732022-12-22T02:35:30ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79462015-09-0122549951210.5194/npg-22-499-2015Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphsK. Vasudevan0M. Cavers1A. Ware2Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1N4, CanadaDepartment of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1N4, CanadaDepartment of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N 1N4, CanadaEarthquake 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 non-linear dynamics on a directed graph of a sequence of earthquakes. For directed graphs with certain properties, the Kuramoto model yields synchronization, and inclusion of non-local 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.http://www.nonlin-processes-geophys.net/22/499/2015/npg-22-499-2015.pdf |
| spellingShingle | K. Vasudevan M. Cavers A. Ware Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs Nonlinear Processes in Geophysics |
| title | Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs |
| title_full | Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs |
| title_fullStr | Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs |
| title_full_unstemmed | Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs |
| title_short | Earthquake sequencing: chimera states with Kuramoto model dynamics on directed graphs |
| title_sort | earthquake sequencing chimera states with kuramoto model dynamics on directed graphs |
| url | http://www.nonlin-processes-geophys.net/22/499/2015/npg-22-499-2015.pdf |
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