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Polyglot entrainment for higher dimensional neuronal models.

Lawan Wijayasooriya1, Emel Khan2, Rakhshanda Qasim2

  • 1Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30303, USA.

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This study introduces polyglot entrainment in higher-dimensional nonlinear systems, extending previous findings in 2D models. It reveals conditions for this synchronization phenomenon near Hopf bifurcations in complex biological models.

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Area of Science:

  • Dynamical Systems
  • Nonlinear Dynamics
  • Computational Neuroscience

Background:

  • Biological oscillator entrainment is a fundamental problem in synchronization.
  • Polyglot entrainment, a novel mechanism, was previously studied only in 2D slow-fast systems near Hopf bifurcations (HBs).

Purpose of the Study:

  • To investigate polyglot entrainment in higher-dimensional nonlinear systems.
  • To extend the understanding of polyglot entrainment beyond 2D models and explore its occurrence in conductance-based models.

Main Methods:

  • Utilized dynamical systems theory and tools.
  • Analyzed the geometric structure of null surfaces.
  • Investigated higher-dimensional conductance-based models, including the Hodgkin-Huxley model and its reduced version.

Main Results:

  • Polyglot entrainment was observed in higher-dimensional models.
  • Identified conditions for polyglot entrainment near Hopf bifurcations.
  • Found that polyglot entrainment occurs when the unforced system acts as a damped oscillator with a fixed point near a cubic-like manifold.

Conclusions:

  • Polyglot entrainment is a generalizable phenomenon in higher-dimensional nonlinear systems.
  • The study provides insights into the underlying mechanisms and conditions for polyglot entrainment.
  • Findings contribute to understanding synchronization in complex biological systems.