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Oscillation behavior driven by processing delay in diffusively coupled inactive systems: Cluster synchronization and

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Processing delay in complex systems can induce Hopf bifurcation, leading to rich oscillatory behavior and multistable states. This finding is crucial for understanding and controlling synchronization in oscillatory networks.

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Area of Science:

  • Complex Systems Dynamics
  • Nonlinear Systems Theory
  • Network Science

Background:

  • Coupling delays significantly influence the behavior of complex systems.
  • Processing delay, a specific type of coupling delay, has not been fully explored in nonlinear systems.

Purpose of the Study:

  • To investigate the impact of processing delay on the steady state of general nonlinear systems.
  • To demonstrate how processing delay can lead to Hopf bifurcation and oscillatory dynamics.
  • To explore phenomena like multistability and size-dependent cluster synchronization.

Main Methods:

  • Derivation of analytical conditions for inducing an oscillatory regime.
  • Numerical simulations on various oscillator networks to confirm theoretical findings.

Main Results:

  • Processing delay can drive general nonlinear systems to Hopf bifurcation, resulting in sustained oscillations.
  • The study identified conditions for achieving oscillatory behavior.
  • Multistable states and size-dependent cluster synchronization were observed as consequences of processing delay.

Conclusions:

  • Processing delay is a critical factor in the dynamics of complex systems.
  • Understanding processing delay is key to advancing dynamical control and synchronization in oscillatory networks.