Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis and Predictability for Tipping Points with Leading-Order
  Nonlinear Terms   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.

22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con