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Quasipotentials for coupled escape problems and the gate-height bifurcation.

Peter Ashwin1, Jennifer Creaser1, Krasimira Tsaneva-Atanasova2

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Researchers computed quasipotentials for coupled bistable systems to analyze noise-induced transitions. They identified global bifurcations in "gates" that signal qualitative changes in escape properties for non-gradient systems with small noise.

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Area of Science:

  • Dynamical systems theory
  • Non-equilibrium statistical physics
  • Computational physics

Background:

  • Estimating escape statistics in noisy systems often relies on potential landscapes.
  • Freidlin-Wentzell quasipotential (QP) offers a more general approach but is computationally challenging and reference-dependent.
  • Analyzing transitions in coupled bistable units, especially those lacking a clear potential, requires advanced methods.

Purpose of the Study:

  • To develop and apply methods for computing quasipotentials in coupled bistable systems.
  • To analyze noise-induced transitions using quasipotentials, particularly in systems without an explicit potential.
  • To investigate the role of "gates" in understanding escape rates and their bifurcations.

Main Methods:

  • Numerical solution of a Hamilton-Jacobi-Bellman type problem to compute quasipotentials.
  • Analysis of noise-induced transitions via quasipotentials in non-potential coupled systems.
  • Identification and analysis of "gates" (minimal QP points on basin boundaries) to determine escape rates.

Main Results:

  • Successfully computed quasipotentials for coupled bistable units, enabling analysis of noise-induced transitions.
  • Demonstrated the utility of quasipotentials in systems lacking a defined potential landscape.
  • Observed global gate-height bifurcations as a function of coupling strength, indicating qualitative shifts in escape dynamics.

Conclusions:

  • Quasipotential computation provides a powerful tool for understanding escape dynamics in complex, non-gradient systems.
  • Gate bifurcations represent a generic mechanism for qualitative transitions in the escape properties of parametrized systems with small noise.
  • The study advances the analysis of noise-induced transitions and escape phenomena in non-equilibrium systems.