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This study presents an adaptive control scheme to achieve desynchronization in coupled networks, even with feedback delays. Controlling a single cluster is insufficient for networks with three or more clusters.

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Area of Science:

  • Neuroscience
  • Control Theory
  • Network Science

Background:

  • Coupled network synchronization plays a crucial role in various biological and artificial systems.
  • Achieving controlled desynchronization is essential for understanding and treating neurological disorders.
  • Existing control schemes often struggle with feedback delays and partial network control.

Purpose of the Study:

  • To introduce a novel adaptive control scheme for achieving desynchronization in coupled networks with feedback delays.
  • To investigate the scheme's efficacy in partially controlled networks, including those with multiple clusters.
  • To analyze the impact of time delays and inter-connectivity on network stability.

Main Methods:

  • Development of an adaptive control scheme incorporating feedback delay.
  • Validation using numerical and rigorous analysis of the transcendental characteristic equation.
  • Application to coupled neuronal networks with two and multiple clusters.
  • Investigation of stability for incoherent states under varying delay and connectivity parameters.

Main Results:

  • The proposed adaptive control scheme effectively achieves desynchronization in coupled networks with feedback delays.
  • Controlling only one cluster is demonstrated to be ineffective for desynchronization in networks with three or more clusters.
  • Time delay and inter-connectivity significantly influence the stability of incoherent states.

Conclusions:

  • The adaptive control scheme offers a viable method for inducing desynchronization in complex networks.
  • Understanding the limitations of single-cluster control is critical for multi-cluster network interventions.
  • Findings provide insights into deep brain stimulation and suggest adaptive feedback strategies for neurodegenerative disease treatment.