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Escape statistics for parameter sweeps through bifurcations.

Nicholas J Miller1, Steven W Shaw

  • 1Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48824, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 12, 2012
PubMed
Summary
This summary is machine-generated.

This study analyzes system dynamics during parameter sweeps with noise, focusing on "escape events" from stable to unstable states. Understanding these events aids system identification and sensing, especially in microelectromechanical systems.

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Area of Science:

  • Nonlinear dynamics
  • Stochastic processes
  • System identification

Background:

  • Systems undergoing parameter sweeps can exhibit complex dynamics near bifurcation points.
  • Noise significantly influences system behavior, especially during transitions.
  • Understanding escape events is crucial for applications like sensing and system identification.

Purpose of the Study:

  • To analyze the dynamics of systems with parameter sweeps through bifurcation points in the presence of noise.
  • To investigate local codimension-one bifurcations leading to large excursions (escape events).
  • To develop methods for system identification and sensing using information from these escape events.

Main Methods:

  • Stochastic normal forms for dynamic saddle-node and subcritical pitchfork bifurcations.
  • Analysis of time-varying bifurcation parameters and additive noise.
  • Formulation and numerical solution for the distribution of escape events.
  • Analytical approximations for delayed bifurcations.

Main Results:

  • Characterization of escape event distributions under noise and parameter sweeps.
  • Identification of delayed bifurcations where escape occurs beyond quasistatic points.
  • Demonstration of amplitude jumps during parameter sweeps due to these bifurcations.
  • Relevance of noise-induced bifurcations in nano- and microelectromechanical systems (NEMS/MEMS).

Conclusions:

  • Noise-induced bifurcations and escape events are critical phenomena in systems with parameter sweeps.
  • The developed methods provide insights into system dynamics and enable applications in sensing and identification.
  • Delayed bifurcations and amplitude jumps are significant in NEMS/MEMS, highlighting the role of noise.