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Delayed dynamical systems: networks, chimeras and reservoir computing.

Joseph D Hart1,2, Laurent Larger3, Thomas E Murphy1,4

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Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|July 23, 2019
PubMed
Summary
This summary is machine-generated.

We developed a systematic method to link time delay dynamics with coupled oscillator networks. This approach uses field-programmable gate arrays to explore complex synchronization patterns in diverse network structures.

Keywords:
chimerasdelayed dynamical systemnetworksreservoir computing

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Area of Science:

  • Nonlinear dynamics
  • Complex systems
  • Network science

Background:

  • Time-delay systems exhibit complex dynamics, with applications in optoelectronic feedback loops for phenomena like chimeras and reservoir computing.
  • Digital signal processing has enhanced the study of delayed dynamical systems.
  • Previous research highlighted spatio-temporal representations for understanding time-delay system dynamics.

Purpose of the Study:

  • To establish a systematic approach for understanding the relationship between time delay dynamics and networks of coupled oscillators.
  • To extend the capabilities of implementing networks with arbitrary topologies for studying complex dynamics.
  • To explore synchronization patterns in various network configurations.

Main Methods:

  • Utilizing field-programmable gate arrays (FPGAs) to implement networks with arbitrary topologies.
  • Designing appropriate filters and multiple time delays within the FPGA architecture.
  • Investigating dynamics on networks with identical nodes, parameter heterogeneities, and varying topologies.

Main Results:

  • Demonstrated the extension of capabilities for implementing arbitrary network topologies.
  • Enabled exploration of complex dynamics, including synchronization patterns, in diverse network structures.
  • Facilitated the control over formation and evolution of synchrony patterns by altering network topology and parameters.

Conclusions:

  • The developed FPGA-based architecture significantly enhances the study of nonlinear dynamics in delay systems.
  • This approach provides a flexible platform for exploring synchronization phenomena in complex networks.
  • The findings open new avenues for understanding and controlling emergent behaviors in coupled oscillator systems.