Intermittent dynamics in complex systems driven to depletion

From earthquakes driven by continental drift to businesses altering their strategies in response to customers’ behaviour, many complex systems exhibit highly unpredictable dynamics, fluctuating episodically between periods of relative quiescence and bursts of activity. Of particular interest are systems that exhibit such behaviour as they gradually settle into an ultimately inert or static phase. In an attempt to understand and possibly predict such dynamics, LML Fellow Isaac Pérez Castillo and Juan Escobar have explored a generic model designed to capture such dynamics in a minimal way. They find that it exhibits a transition from a regime of continuous dynamics to one characterised by strongly intermittent behaviour. In the latter regime, the size of events or “avalanches” can be predicted with some degree of success, despite the stochastic nature of the process.
Although the model is highly abstract, the study also shows that it accounts accurately for the way cinema theatres phase out the showing of new films as the number of attendees falls over time. The phase out doesn’t occur gradually, but in a highly erratic way, with a small drop in numbers provoking a highly unpredictable response. Castillo and Escobar show that the model accounts closely for data for 3,000 films over a 30 year period, and matches the distribution of events by size over almost three orders of magnitude.
The paper is available at

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