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Isostables for Stochastic Oscillators.

Alberto Pérez-Cervera1, Benjamin Lindner2, Peter J Thomas3

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This summary is machine-generated.

Researchers defined a stochastic isostable coordinate for noisy oscillators, completing a phase-amplitude description. This framework aids understanding of stochastic limit cycle dynamics and noise-induced oscillations.

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Stochastic Processes

Background:

  • The asymptotic phase of stochastic oscillators was previously defined using the backward Kolmogorov operator.
  • A complete phase-amplitude description for noisy oscillators is essential for understanding their dynamics.

Purpose of the Study:

  • To define the stochastic isostable coordinate for noisy oscillators.
  • To extend the phase-amplitude description of stochastic oscillators.
  • To provide a framework for stochastic limit cycle dynamics.

Main Methods:

  • Defining the stochastic isostable coordinate as a specific eigenfunction of the backward Kolmogorov operator.
  • Utilizing complex eigenvalues with least negative nontrivial real parts.

Main Results:

  • The stochastic isostable coordinate was successfully defined.
  • This definition completes the phase-amplitude description for stochastic oscillators.
  • The results suggest a framework encompassing noise-induced oscillations.

Conclusions:

  • The stochastic isostable coordinate provides a new tool for analyzing noisy oscillators.
  • This work advances the understanding of stochastic limit cycle dynamics.
  • The framework may explain noise-induced oscillations in various systems.