Long transient dynamics in a stochastic ecological system

Dr. Jody Reimer, University of Utah
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Abstract: Recent theoretical work has highlighted several mechanisms giving rise to so-called ``long transient'' dynamics, where the system trajectory stays near a non-attracting state for a long time before suddenly undergoing a regime shift. We consider a simple ecological model with a saddle-node bifurcation. For parameter values above the bifurcation threshold, the model exhibits bistability, while for values below it, the model has long transient dynamics near a so-called ghost attractor. In the deterministic case, these regimes have distinct dynamical properties. In the stochastic case, both regimes can produce similar time series, fluctuating around one state for several generations before suddenly switching to another. We first explore the effect of stochasticity on our ability to infer underlying mechanisms from time-series data. We then quantify the expected duration of the long transient using mean first passage time (MFPT) theory, extending it to the case of the ghost attractor. We find that long transients can be highly sensitive to noise, and that the behavior of the stochastic model can differ substantially from that of the deterministic model. We also show that the MFPT varies continuously with the bifurcation parameter, obscuring the difference between the bistable and long transient regimes, making inference difficult, but also not necessarily important in practice.