An iterative action minimizing method for computing optimal paths in stochastic dynamical systems

Abstract

We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by minimizing the effective action in a corresponding deterministic Hamiltonian system. The numerical method presented here involves using an iterative scheme for solving a two-point boundary value problem for the Hamiltonian system. We validate our method by applying it to both continuous stochastic systems, such as nonlinear oscillators governed by the Duffing equation, and finite discrete systems, such as epidemic problems, which are governed by a set of master equations. Furthermore, we demonstrate that this method is capable of dealing with stochastic systems of delay differential equations.

20 pages, 8 figures

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• Degree Dispersion Increases the Rate of Rare Events in Population Networks
• Enhancement of large fluctuations to extinction in adaptive networks
• Most probable transition paths in piecewise-smooth stochastic differential equations
• Large order fluctuations, switching, and control in complex networks
• Taming the diffusion approximation through a controlling-factor WKB method
• Rare events in networks with internal and external noise
• Large deviations for Gaussian diffusions with delay
• SIS model of disease extinction on heterogeneous directed population networks
• Large and small fluctuations in oscillator networks from heterogeneous and correlated noise
• Rare extinction events in cyclic predator-prey games
• Asymmetric noise-induced large fluctuations in coupled systems
• Metastable transitions in inertial Langevin systems: what can be different from the overdamped case?
• Going with the flow: enhancing stochastic switching rates in multi-gyre systems