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Differential relays are used to protect generators, buses, and transformers by comparing electrical quantities at different points. When a fault occurs, the difference in current between the two points triggers the relay to operate, opening the circuit breaker. Under normal conditions, the current entering (i1) and leaving (i2) a generator are equal. When a fault occurs, however, these currents become unequal, and the difference current flows in the relay operating coil, causing the relay to...
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Zero-lag synchronization despite inhomogeneities in a relay system.

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This study explores zero-lag synchronization in delayed coupled neurons using a relay neuron. Synchrony is maintained with symmetric inhomogeneity but lost if symmetry is broken, with analytical results provided for phase lag.

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Area of Science:

  • Computational Neuroscience
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • Delayed coupled neurons are fundamental in neural networks.
  • Achieving zero-lag synchronization is crucial for information processing.
  • Indirect coupling via a relay neuron offers a novel synchronization strategy.

Purpose of the Study:

  • To investigate the robustness of zero-lag synchronization in a relay neuron system.
  • To analyze the impact of inhomogeneity on synchrony.
  • To determine conditions for preserving or losing synchrony.

Main Methods:

  • Development of a Poincaré map to analyze system dynamics.
  • Investigation of neuron and synaptic parameter inhomogeneity.
  • Analytical derivation of phase lag for asymmetric systems.

Main Results:

  • Zero-lag synchrony is robust to symmetric inhomogeneity, which can even enhance synchrony.
  • Asymmetric inhomogeneity breaks the system's symmetry, leading to loss of zero-lag synchrony.
  • Analytical solutions for phase lag were derived for asymmetric cases.

Conclusions:

  • The symmetry of the relay system is critical for maintaining zero-lag synchronization.
  • Inhomogeneity's effect on synchrony depends on its impact on system symmetry.
  • The study provides insights into controlling and understanding neural synchrony.