Enhancing noise-induced switching times in systems with distributed delays

Area of Science:

• Physics
• Nonlinear Dynamics
• Stochastic Processes

Background:

• Understanding noise-induced switching is crucial for systems with time delays.
• Existing models often simplify delay distributions, limiting applicability.

Purpose of the Study:

• To develop a general method for calculating noise-induced switching rates in systems with delay-distributed kernels and Gaussian noise.
• To derive analytical results for switching rates, particularly for small mean time delays.

Main Methods:

• A general variational formulation for switching rate calculation was derived.
• Equations of motion and boundary conditions representing the optimal escape path were obtained.
• Analytical solutions were derived for uniform and bi-modal delay distributions.

Main Results:

• The study provides explicit analytical results for switching rates with small mean time delays.
• Increasing the width of the delay distribution increases switching times.
• This effect is more pronounced for bi-modal (two-peak) distributions.

Conclusions:

• The derived method accurately predicts noise-induced switching rates.
• Delay distribution width significantly influences system escape time.
• Analytical predictions show excellent agreement with numerical simulations.