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This study introduces a new method for analyzing input-induced oscillations in dynamical systems. The isostable coordinate framework accurately predicts bifurcations and phase-locking in coupled systems, applicable to circadian and neural physiology.

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Area of Science:

  • Dynamical Systems Theory
  • Nonlinear Dynamics
  • Computational Neuroscience

Background:

  • Reduced order modeling is crucial for analyzing complex oscillatory systems.
  • Existing methods often fail for oscillations induced by external inputs or coupling.
  • Input-induced oscillations are prevalent in biological and physical systems.

Purpose of the Study:

  • To develop a robust framework for reduced order modeling of input-induced oscillations.
  • To accurately predict bifurcations and phase-locking in coupled dynamical systems.
  • To extend these techniques to systems relevant to circadian and neural physiology.

Main Methods:

  • Leveraging the isostable coordinate framework for high-accuracy model reduction.
  • Employing asymptotic expansion of isostable coordinate dynamics near Hopf bifurcations.
  • Utilizing an adaptive phase-amplitude reduction for excitable systems.

Main Results:

  • Successfully identified reduced equations for input-induced oscillations.
  • Predicted coupling-induced bifurcations leading to stable oscillations.
  • Accurately determined steady-state phase-locking relationships.

Conclusions:

  • The proposed isostable coordinate framework effectively models input-induced oscillations.
  • The methods are applicable to diverse coupled dynamical systems, including those in physiology.
  • This work advances the analysis of oscillations in systems driven by external factors.