A primer on noise-induced transitions in applied dynamical systems. (English) Zbl 1408.37089
Summary: Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in large behavioral changes such as transitions between or escapes from quasi-stable states. These transitions can correspond to critical events such as failures or extinctions that make them essential phenomena to understand and quantify, despite the fact that their occurrence is rare. This article will provide an overview of the theory underlying the dynamics of rare events for stochastic models along with some example applications.
MSC:
| 37H10 | Generation, random and stochastic difference and differential equations |
| 37N25 | Dynamical systems in biology |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 92D30 | Epidemiology |
| 92D40 | Ecology |
Keywords:
escape; extinction; mean exit time; large deviation theory; mode-locked lasers; noise-induced transitions; optimal path; rare events; stochasticity; epidemiology; bit error ratiosReferences:
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