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Interaction Control to Synchronize Non-synchronizable Networks.

Malte Schröder1, Sagar Chakraborty2, Dirk Witthaut3,4

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We introduce interaction control to synchronize complex networks, even those previously considered non-synchronizable. This method localizes interactions, enabling stable synchronization across diverse network topologies.

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Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Synchronization is a fundamental collective behavior in networked systems, crucial for their function.
  • Network synchronizability depends on unit dynamics, interaction topology, and strength.
  • Certain networks with chaotic units and specific topologies are non-synchronizable.

Purpose of the Study:

  • To propose and demonstrate a novel method, interaction control, to induce synchronization in complex networks.
  • To generalize transient uncoupling for controlling collective dynamics.
  • To synchronize non-synchronizable networks.

Main Methods:

  • Introducing the concept of interaction control, a method to manage network interactions.
  • Applying a simple binary control to localize interactions in state space.
  • Analyzing the synchronization of networks with varying topologies and interaction strengths.

Main Results:

  • Non-synchronizability is prevalent in many real-world networks.
  • Interaction control effectively synchronizes networks, including previously non-synchronizable ones.
  • A fixed control scheme enables stable synchronization across all connected networks, irrespective of topology.

Conclusions:

  • Interaction control provides a robust method for achieving desired collective dynamics in complex networks.
  • This approach simplifies the design of synchronized systems, even without full knowledge of network topology.
  • The findings have significant implications for biological and self-organizing technical systems.