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Updated: Aug 13, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Stochastic dynamics in a two-dimensional oscillator near a saddle-node bifurcation
M E Inchiosa1, V In, A R Bulsara
1Space and Naval Warfare Systems Center San Diego, Code D363, 49590 Lassing Road, San Diego, California 92152-6147, USA. inchiosa@spawar.navy.mil
Summary
This study analyzes nonlinear amplifier dynamics using superconducting quantum interference devices. We found enhanced sensitivity to magnetic signals and validated an integrate-fire model for oscillatory behavior.
Area of Science:
- Nonlinear Dynamics
- Quantum Electronics
- Computational Neuroscience
Background:
- Nonlinear amplifiers, like the two-junction superconducting quantum interference device (SQUID), exhibit complex dynamics.
- These systems can transition between stable states and oscillatory "running states" via bifurcations.
- Enhanced sensitivity to weak magnetic signals is observed near the onset of spontaneous oscillations.
Purpose of the Study:
- To analytically approximate the oscillatory behavior of nonlinear amplifiers past a saddle-node bifurcation.
- To compute the oscillation period and validate scaling laws.
- To model the system's dynamics using an integrate-fire model and compare with numerical simulations.
Main Methods:
- Center manifold technique applied to the oscillator equations.
- Analytical approximation of oscillatory behavior near bifurcation.
- Renewal theory used for calculating interspike interval and power spectral density.
- Comparison with results from numerical simulations.
Main Results:
- Analytical approximation of oscillation period obeying standard scaling laws.
- Successful representation of dynamics using an integrate-fire model.
- High agreement between theoretical predictions (interspike interval, power spectral density) and numerical simulations.
- Observed noise-lowering effects like injection locking and heterodyning when driven by sinusoids.
Conclusions:
- The center manifold technique provides an effective analytical tool for understanding nonlinear amplifier dynamics near bifurcations.
- The integrate-fire model accurately captures the oscillatory behavior and statistical properties of the system.
- The study demonstrates a link between nonlinear dynamics in physical systems and computational neuroscience models.
- Exploitation of these dynamics offers potential for enhanced magnetic signal detection and signal processing.
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