Using a system of two FitzHugh-Nagumo units, we demonstrate the occurrence of riddled basins of attraction in delay-coupled systems as the coupling between the units is increased. We characterize riddled basins using the uncertainty exponent which is a measure of the dimensions of the basin boundary. Additionally, we show that the phase space can be partitioned into pure and mixed regions, where initial conditions in the pure regions certainly avoid the generation of extreme events, while initial conditions in the mixed region may or may not exhibit such events. This implies that any tiny perturbation of initial conditions in the mixed region could yield the emergence of extreme events because the latter state possesses a riddled basin of attraction.
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March 2018
Research Article|
March 19 2018
Riddled basins of attraction in systems exhibiting extreme events Available to Purchase
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Multistability and Tipping
Arindam Saha
;
Arindam Saha
a)
Theoretical Physics/Complex Systems, ICBM, University of Oldenburg
, 26129 Oldenburg, Germany
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Ulrike Feudel
Ulrike Feudel
b)
Theoretical Physics/Complex Systems, ICBM, University of Oldenburg
, 26129 Oldenburg, Germany
Search for other works by this author on:
Arindam Saha
a)
Theoretical Physics/Complex Systems, ICBM, University of Oldenburg
, 26129 Oldenburg, Germany
Ulrike Feudel
b)
Theoretical Physics/Complex Systems, ICBM, University of Oldenburg
, 26129 Oldenburg, Germany
a)
Electronic mail: [email protected]
b)
Electronic mail: [email protected]
Chaos 28, 033610 (2018)
Article history
Received:
November 06 2017
Accepted:
February 25 2018
Citation
Arindam Saha, Ulrike Feudel; Riddled basins of attraction in systems exhibiting extreme events. Chaos 1 March 2018; 28 (3): 033610. https://doi.org/10.1063/1.5012134
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