Name
Abstract | ||
|---|---|---|
Tipping points have been actively studied in various applications as well as from a mathematical viewpoint. A main technique to theoretically understand early-warning signs for tipping points is to use the framework of fast-slow stochastic differential equations. A key assumption in many arguments for the existence of variance and auto-correlation growth before a tipping point is to use a linearization argument, i.e., the leading-order term governing the deterministic (or drift) part of stochastic differential equation is linear. This assumption guarantees a local approximation via an Ornstein-Uhlenbeck process in the normally hyperbolic regime before, but sufficiently bounded away from, a bifurcation. In this paper, we generalize the situation to leading-order nonlinear terms for the setting of one fast variable. We work in the quasi-steady regime and prove that the fast variable has a well-defined stationary distribution and we calculate the scaling law for the variance as a bifurcation-induced tipping point is approached. We cross-validate the scaling law numerically. Furthermore, we provide a computational study for the predictability using early-warning signs for leading-order nonlinear terms based upon receiver-operator characteristic curves. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1142/s0218127418501031 | International Journal of Bifurcation and Chaos |
Field | DocType | Volume |
Applied mathematics,Predictability,Nonlinear system,Stochastic differential equation,Stationary distribution,Classical mechanics,Mathematics,Linearization,Tipping point (climatology),Bounded function,Bifurcation | Journal | 28 |
Issue | Citations | PageRank |
8 | 0 | 0.34 |
References | Authors | |
1 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Francesco Romano | 1 | 0 | 2.37 |
| Christian Kuehn | 2 | 90 | 12.21 |