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Delay-induced synchrony in complex networks with conjugate coupling.

M Manju Shrii1, D V Senthilkumar, J Kurths

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We show that delayed conjugate coupling in networks can induce and enhance synchronous chaos, even in systems without inherent synchronization. This method offers a novel approach to controlling complex dynamical systems.

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Area of Science:

  • Dynamical Systems and Network Science
  • Nonlinear Dynamics
  • Computational Neuroscience

Background:

  • Coupled dynamical systems often exhibit complex behaviors like chaos and synchronization.
  • Delay coupling is a common phenomenon in real-world systems, influencing their dynamics.
  • Master Stability Formalism (MSF) is a powerful tool for analyzing synchronization in networks.

Purpose of the Study:

  • To investigate the effects of delayed conjugate coupling on synchronization in complex networks.
  • To demonstrate that conjugate coupling can replace delay coupling in inducing delay-induced phenomena.
  • To explore the capability of delayed conjugate coupling in inducing and enhancing synchronization.

Main Methods:

  • Utilizing the Master Stability Formalism (MSF) framework.
  • Analyzing time-continuous dynamical systems in a network configuration.
  • Employing paradigmatic models such as the Rössler system and Hindmarsh-Rose neuron.

Main Results:

  • Stable synchronous chaos is demonstrated in delay-coupled networks.
  • Conjugate coupling is shown to effectively substitute for delay coupling in retrieving delay-induced phenomena.
  • Delayed conjugate coupling induces synchronization in previously unsynchronized networks and expands the synchronization parameter space.

Conclusions:

  • Delayed conjugate coupling offers a versatile method for controlling synchronization in complex networks.
  • This approach provides a means to induce and enhance synchronization beyond the capabilities of traditional coupling methods.
  • The findings are robust and demonstrated across different dynamical systems.