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Laser chimeras as a paradigm for multistable patterns in complex systems.

Larger L, Penkovsky B, Maistrenko Y - Nat Commun (2015)

Bottom Line: Necessary features of the network for the emergence of such complex but structured motions are non-local and symmetry breaking coupling.We uncover a cascade of higher-order chimeras as a pattern transition from N to N+1 clusters of chaoticity.Finally, we follow visually, as the gain increases, how chimera state is gradually destroyed on the way to apparent turbulence-like system behaviour.

View Article: PubMed Central - PubMed

Affiliation: Institut FEMTO-ST, UMR 6174, Université Bourgogne Franche-Comté, CNRS, 15B avenue des Montboucons, 25030 Besançon, France.

ABSTRACT
A chimera state is a rich and fascinating class of self-organized solutions developed in high-dimensional networks. Necessary features of the network for the emergence of such complex but structured motions are non-local and symmetry breaking coupling. An accurate understanding of chimera states is expected to bring important insights on deterministic mechanism occurring in many structurally similar high-dimensional dynamics such as living systems, brain operation principles and even turbulence in hydrodynamics. Here we report on a powerful and highly controllable experiment based on an optoelectronic delayed feedback applied to a wavelength tuneable semiconductor laser, with which a wide variety of chimera patterns can be accurately investigated and interpreted. We uncover a cascade of higher-order chimeras as a pattern transition from N to N+1 clusters of chaoticity. Finally, we follow visually, as the gain increases, how chimera state is gradually destroyed on the way to apparent turbulence-like system behaviour.

No MeSH data available.


Related in: MedlinePlus

Probability of occurrence for N-headed chimera.These probabilities for different number of heads are calculated from the asymptotic N-headed chimera states emerged from many different random initial conditions, and for three different values of δ (horizontal cut in Fig. 2).
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f5: Probability of occurrence for N-headed chimera.These probabilities for different number of heads are calculated from the asymptotic N-headed chimera states emerged from many different random initial conditions, and for three different values of δ (horizontal cut in Fig. 2).

Mentions: Figure 2a reveals that model (Equation 3) is highly multistable for small and intermediate ɛ. This suggests to explore the basins of attraction of the different co-existing attractors. Since time-delayed systems are infinite dimensional through their initial conditions being functional {x0(s)/s∈[0,1]}, a precise topological characterization of the basins structure is not directly possible. One can however try to estimate the relative size (measure) of the basins in terms of occurrence probability for each possible solution, after resetting many different random initial conditions. This is illustrated in Fig. 5, which shows the evolution versus ɛ of the probability occurrence for Nσ-headed chimera for three fixed δ values, with Nσ=0–5 (0 corresponding to chaotic breather). Each probability has been calculated with 300 different initial noisy conditions x0(s) (uniform amplitude distribution of x∈[−1;1]).


Laser chimeras as a paradigm for multistable patterns in complex systems.

Larger L, Penkovsky B, Maistrenko Y - Nat Commun (2015)

Probability of occurrence for N-headed chimera.These probabilities for different number of heads are calculated from the asymptotic N-headed chimera states emerged from many different random initial conditions, and for three different values of δ (horizontal cut in Fig. 2).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4510973&req=5

f5: Probability of occurrence for N-headed chimera.These probabilities for different number of heads are calculated from the asymptotic N-headed chimera states emerged from many different random initial conditions, and for three different values of δ (horizontal cut in Fig. 2).
Mentions: Figure 2a reveals that model (Equation 3) is highly multistable for small and intermediate ɛ. This suggests to explore the basins of attraction of the different co-existing attractors. Since time-delayed systems are infinite dimensional through their initial conditions being functional {x0(s)/s∈[0,1]}, a precise topological characterization of the basins structure is not directly possible. One can however try to estimate the relative size (measure) of the basins in terms of occurrence probability for each possible solution, after resetting many different random initial conditions. This is illustrated in Fig. 5, which shows the evolution versus ɛ of the probability occurrence for Nσ-headed chimera for three fixed δ values, with Nσ=0–5 (0 corresponding to chaotic breather). Each probability has been calculated with 300 different initial noisy conditions x0(s) (uniform amplitude distribution of x∈[−1;1]).

Bottom Line: Necessary features of the network for the emergence of such complex but structured motions are non-local and symmetry breaking coupling.We uncover a cascade of higher-order chimeras as a pattern transition from N to N+1 clusters of chaoticity.Finally, we follow visually, as the gain increases, how chimera state is gradually destroyed on the way to apparent turbulence-like system behaviour.

View Article: PubMed Central - PubMed

Affiliation: Institut FEMTO-ST, UMR 6174, Université Bourgogne Franche-Comté, CNRS, 15B avenue des Montboucons, 25030 Besançon, France.

ABSTRACT
A chimera state is a rich and fascinating class of self-organized solutions developed in high-dimensional networks. Necessary features of the network for the emergence of such complex but structured motions are non-local and symmetry breaking coupling. An accurate understanding of chimera states is expected to bring important insights on deterministic mechanism occurring in many structurally similar high-dimensional dynamics such as living systems, brain operation principles and even turbulence in hydrodynamics. Here we report on a powerful and highly controllable experiment based on an optoelectronic delayed feedback applied to a wavelength tuneable semiconductor laser, with which a wide variety of chimera patterns can be accurately investigated and interpreted. We uncover a cascade of higher-order chimeras as a pattern transition from N to N+1 clusters of chaoticity. Finally, we follow visually, as the gain increases, how chimera state is gradually destroyed on the way to apparent turbulence-like system behaviour.

No MeSH data available.


Related in: MedlinePlus