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Stability and synchronization in neural network with delayed synaptic connections.

A Brice Azangue1, E B Megam Ngouonkadi1,2, M Kabong Nono1

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Summary
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This study explores complex network stability using the master stability function and the Hindmarsh-Rose neuronal model. Hybrid coupling demonstrates superior stability and synchronization compared to electrical or chemical couplings alone.

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Area of Science:

  • Neuroscience
  • Complex Systems
  • Network Science

Background:

  • Investigating synchronous states in complex networks is crucial for understanding emergent behaviors.
  • Neuronal models are essential for simulating network dynamics and stability.
  • Time-delayed couplings introduce complexity in network synchronization.

Purpose of the Study:

  • To analyze the stability of synchronous states in complex networks with various coupling types.
  • To compare the stability and synchronization properties of electrical, chemical, and hybrid couplings.
  • To determine the impact of time delays on network stability.

Main Methods:

  • Utilized the master stability function technique.
  • Employed the extended Hindmarsh-Rose neuronal model.
  • Analyzed dynamics using the maximum Lyapunov exponent and eigenvalues.

Main Results:

  • Electrical coupling showed mixed stable and unstable states, tunable by parameters.
  • Chemical coupling presented challenges in achieving stable states.
  • Hybrid coupling exhibited enhanced overall system stability and synchronization compared to individual couplings.

Conclusions:

  • Hybrid coupling offers a robust approach to achieving stable and synchronized complex networks.
  • The stability analysis provides insights into network topology and coupling strategies.
  • Synchronized network states correlate with stable system dynamics.