Chimera States in Nonlinear Systems with Multiple Delayed Feedbacks - - PowerPoint PPT Presentation

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Chimera States in Nonlinear Systems with Multiple Delayed Feedbacks - - PowerPoint PPT Presentation

Jan 22, 2023 304 likes •682 views

Chimera States in Nonlinear Systems with Multiple Delayed Feedbacks Bogdan Penkovsky FEMTO-ST Institute, France in collaboration with D. Brunner R. Levchenko E.Schll L. Larger Y. Maistrenko Delays affect your life in a number of ways

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Chimera States in Nonlinear Systems with Multiple Delayed Feedbacks

Bogdan Penkovsky

FEMTO-ST Institute, France in collaboration with

  • D. Brunner R. Levchenko E.Schöll L. Larger Y. Maistrenko
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Delays affect your life in a number of ways

Long-distance light propagation Propagation delays in the brain Traffic jams Hot-cold water control in a shower!

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Delayed-feedback Systems

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Delay Differential Equations (DDEs)

  • x(t) is dynamical variable
  • is delay time
  • is system response time
  • f (x) is nonlinear transformation
  • is feedback gain

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Dynamical regimes. Bifurcations

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Applications of NL Delay Dynamics

Chaos communications, 1995 High spectral purity microwave

  • scillators, 1994

Photonic Reservoir Computing, 2012 Chimera study in networks of virtual

  • scillators, 2013

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Understanding NL Dynamical Networks is Crucial

  • Power grids
  • Internet
  • Social networks
  • Bird swarms
  • Brain

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* Image from S. H. Strogatz (Nature, 2001.)

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What are chimeras?

...monstrous fire-breathing creatures

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Chimeras: Kuramoto and Delay Networks

  • Chimera is a network state consisting of incongruent parts:

coherent and chaotic.

Chimera states can arise in many real-world networks

  • Power grids
  • Networks of neurons in the human heart

Leading to failure of the system.

Are chimeras possible in delay systems?

  • Symmetric Kuramoto network
  • Long-range coupling to obtain

a chimera state

*Y. Kuramoto (Nonlin. Phenomena in Complex Sys., 2002.)

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Chimeras in single delay systems

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Experimental Setup For Delay Chimeras

  • Laser light is NL transformed
  • The signal is delayed, filtered
  • The signal is modulating the wavelength of the laser

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Experimental Setup For Delay Chimeras

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Experimental Setup For Delay Chimeras

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System Properties

NL function asymmetry Bistability: low gradient and large gradient

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"Coupling" Induced By Filters

Impulse response function h(t)

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Long-range coupling thanks to the integral term DDE "Coupling": Impulse Response Function

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Network Analogy. Space-Time Representation

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  • Stacking temporal coordinates
  • Virtual space
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Network Analogy. Space-Time Representation

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Theory vs Experiment

  • Exist over long time
  • Excellent agreement between the model and experiment
  • L. Larger, B. Penkovsky, Y. Maistrenko (PRL 2013; Nature Comm.

2015)

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  • First demonstration of chimeras in delay systems
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Multiheaded Chimeras

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  • Tunable number of heads
  • Increased system complexity
  • Coexistence of chimeras with

different number of heads

  • Can be possibly used in

applications

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Double delay systems

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System with two delays

Brunner et al. arxiv:1712.03283

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System with two delays

Brunner et al. arxiv:1712.03283

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Coherent core

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Simulation Experiment

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Incoherent core

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Simulation Experiment

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Dissipative solitons:

  • ptical memory medium?

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arxiv:1712.03283

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arxiv:1712.03283

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arxiv:1712.03283

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arxiv:1712.03283

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Multistability

Brunner et al. arxiv:1712.03283

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Take-away message

Network

The dynamical behavior on the delay interval can be translated to a network. Those networks allow observation of chimera states and dissipative solitons.

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Applications of Chimera States/Dissipative solitons

Network

Study of synchronization in complex networks:

  • Power grids
  • Networks of neurons in the human heart

Neuromorphic computing

  • Optical memory
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Thank You

FEMTO-ST

www.penkovsky.com

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