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Rössler-network with time delay: Univariate impulse pinning synchronization.

Kun Tian1, Hai-Peng Ren1, Celso Grebogi1

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Summary
This summary is machine-generated.

This study introduces a novel univariate impulse control method to achieve pinning synchronization in coupled Rössler networks with time delays. The research validates a new controller for regulating complex network behavior.

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Area of Science:

  • Chaos Theory
  • Network Synchronization
  • Control Systems

Background:

  • Dynamical systems, like the Rössler system, are fundamental in understanding complex behaviors.
  • Network synchronization is crucial for controlling emergent behaviors in interconnected systems.
  • Pinning control, using a small set of nodes, offers an efficient strategy for network regulation.

Purpose of the Study:

  • To investigate the pinning synchronization of a coupled Rössler network with time delay.
  • To develop and validate a univariate impulse control strategy for network regulation.
  • To honor the scientific contributions of Rössler through research on his benchmark system.

Main Methods:

  • Utilizing Lyapunov theory to establish conditions for asymptotic stability.
  • Developing a univariate impulse control technique for synchronization.
  • Employing network simulations to verify analytical results.

Main Results:

  • A theorem proving the asymptotic stability of synchronization in the Rössler network was derived.
  • The effectiveness of the univariate impulse pinning controller was demonstrated through simulations.
  • Successful synchronization of the coupled Rössler network was achieved.

Conclusions:

  • The proposed univariate impulse control method is effective for achieving pinning synchronization in delayed Rössler networks.
  • The theoretical analysis, supported by simulations, confirms the stability of the synchronized network.
  • This work provides a valuable control strategy for complex dynamical networks.