| Abstract: |
| Transient dynamics--long-lasting but ultimately finite-time behaviors--are ubiquitous in complex stochastic systems. Understanding their underlying mechanisms remains a fundamental challenge. In this talk, we investigate randomly perturbed processes arising in chemical reaction networks and population dynamics, where extinction is inevitable but preceded by long-lived persistence. Using quasi-stationary distributions (QSDs), we characterize these transient dynamics and analyze their asymptotics in the vanishing-noise regime. We show that intrinsic and extrinsic noise can induce fundamentally different transient dynamics, leading to distinct persistence and extinction patterns. We conclude with a discussion of broader implications and open problems. |
|