The aim is to develop a theoretical understanding of the generation and termination of very intense but localized structures in spatially extended excitable systems with applications to two particular extreme events, namely harmful algal blooms (HAB) in the ocean and epileptic seizures (ES) in the human brain. The mechanisms and conditions relevant for the generation and termination of extreme events will be evaluated depending on intrinsic local excitability properties, on spatial coupling properties, and on heterogeneities in space. Besides the usual excitable models we will introduce a novel type of excitable activator-inhibitor systems in which several activators are competing with each other. Furthermore we develop time series analysis techniques that allow a robust quantification of complex interactions in such systems even for short data sets. Data sets from HAB and ES shall be used to verify these pathways of generation and termination of extreme states identified through the model.
a.) Evaluate the conditions of the occurrence and the termination of localized structures depending on the system parameters, on internal (concerning parameters and dynamics of single units) and external (forcing or input signals) heterogeneities in space.
b.) Prediction of these extreme events (ExEvs) in model systems and measured time series.
PIK will contribute in developing time series analysis techniques that allow a robust quantification of complex time-evolving interactions - in terms of both strength and directionality - during the generation and termination of ExEvs in spatially extended excitable systems. Additionally, PIK will contribute in the analysis of HAB and ES data.
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