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Mode locking in periodically forced gradient frequency neural networks.

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We analyzed mode locking in neural networks, finding synchronization regions narrow with increasing complexity. Numerical simulations matched theoretical predictions under weak forcing but deviated at high amplitudes.

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Area of Science:

  • Computational neuroscience
  • Nonlinear dynamics
  • Complex systems

Background:

  • Neural networks exhibit complex dynamics, including mode locking, crucial for information processing.
  • Understanding synchronization in networks of nonlinear oscillators is key to modeling biological systems.
  • Canonical models offer a simplified yet powerful framework for studying neural network dynamics.

Purpose of the Study:

  • To investigate mode locking phenomena in a canonical model of gradient frequency neural networks.
  • To characterize the complete set of driven behaviors under periodic forcing across all parameter regimes.
  • To analyze the influence of forcing amplitude on synchronization patterns.

Main Methods:

  • Utilized a canonical model of nonlinear oscillators with a range of frequencies.
  • Employed periodic forcing to induce and study mode locking.
  • Developed a closed-form approximation for analyzing Arnold tongue characteristics.
  • Conducted numerical simulations to validate analytical findings.

Main Results:

  • The Arnold tongue, representing the k:m synchronization region, was found to narrow as k and m increase.
  • Analytical predictions closely matched numerical simulations for weak forcing amplitudes.
  • Deviations between analysis and simulation emerged at high forcing amplitudes due to multi-mode synchronization.

Conclusions:

  • The canonical model provides valuable insights into mode locking in neural networks.
  • Synchronization complexity increases with higher-order resonances, leading to narrower locking regions.
  • High forcing amplitudes introduce complex interactions, necessitating advanced modeling techniques beyond single-mode analysis.