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Self-Consistent Correlations of Randomly Coupled Rotators in the Asynchronous State.

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We analyze coupled rotators, revealing temporal autocorrelations in asynchronous states. Our theory provides analytical and numerical solutions, applicable to neural networks.

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Area of Science:

  • Complex systems
  • Computational neuroscience
  • Nonlinear dynamics

Background:

  • Biological networks exhibit asynchronous states with temporal correlations.
  • Unidirectionally coupled rotators model complex systems.
  • Understanding these dynamics is crucial for network function.

Purpose of the Study:

  • To derive and solve self-consistent equations for temporal autocorrelations in coupled rotator networks.
  • To validate theoretical models with numerical simulations.
  • To generalize the theory for pulse-coupled systems and neural networks.

Main Methods:

  • Derivation of differential equations for the autocorrelation function.
  • Analytical solutions in limit cases.
  • Numerical solutions and simulations with varying coupling distributions (Gaussian, sparse).
  • Generalization to pulse-coupled units and integrate-and-fire neuron models.

Main Results:

  • The system exhibits pronounced temporal autocorrelations in asynchronous states.
  • Analytical and numerical solutions for the autocorrelation function were obtained.
  • The theory accurately predicts network behavior for different coupling types.
  • Successful application to recurrent networks of spiking neurons.

Conclusions:

  • The derived theory accurately describes temporal autocorrelations in coupled rotator networks.
  • The framework is applicable to both continuous and pulse-coupled systems.
  • This work provides insights into the dynamics of biological and computational neural networks.