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Taming explosive growth through dynamic random links.

Anshul Choudhary1, Vivek Kohar1, Sudeshna Sinha1

  • 1Indian Institute of Science Education and Research (IISER) Mohali, Knowledge City, SAS Nagar, Sector 81, Manauli PO 140 306, Punjab, India.

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Adding random connections to coupled oscillator networks prevents system blow-ups. A critical fraction of random links, dependent on rewiring time, controls this explosive behavior, offering insights for managing complex systems.

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Area of Science:

  • Nonlinear dynamics
  • Complex networks
  • Systems biology

Background:

  • Coupled limit cycle oscillators model diverse systems like neuronal populations and electrical circuits.
  • Network topology significantly influences system dynamics, potentially leading to unbounded trajectories.

Purpose of the Study:

  • Investigate the effect of network topology on coupled oscillator dynamics.
  • Identify mechanisms to control or prevent unbounded system growth (explosive behavior).

Main Methods:

  • Simulated dynamics of coupled limit cycle oscillators on regular ring and random network topologies.
  • Introduced varying fractions of randomized connections within a regular network.
  • Analyzed system trajectories and identified critical thresholds for boundedness.

Main Results:

  • Strong coupling in regular networks leads to trajectories escaping to infinity.
  • Introducing a fraction of randomized connections suppresses unbounded growth.
  • A scaling relationship exists between the critical fraction of random links and network rewiring time-scale.

Conclusions:

  • Dynamically randomizing connections is an effective strategy to control explosive behavior in coupled oscillator systems.
  • The findings provide a mechanism for managing blow-ups in extended oscillatory systems.
  • Results have implications for understanding and controlling complex systems with emergent dynamics.