Rate and Noise-Induced Tipping Working in Concert

Tipping is the rapid, and often irreversible, change in the state of a system. Rate-induced tipping occurswhen a ramp parameter changes rapidly enough to cause the system to tip between co-existing, attracting states, while noise-induced tipping occurs when there are random transitions between two attractors of the underlying deterministic system. This work builds theory for tipping events in low-dimensional dynamical systems with additive noise and time-dependent parameters, in which noise is not vanishingly small. The central question is understanding what information can be extracted from the theory of large deviations for noise levels outside the validity of the approach, where the guiding principles are geometric dynamical systems methods and Monte Carlo simulations. Both tipping mechanisms are first considered within a model of the oceanic carbon cycle, in which the key objective is understanding how the system tips from a stable fixed point to a stable periodic orbit. While rate-induced tipping away from the fixed point is straightforward, the noise-induced tipping is challenging due to a periodic orbit forming the basin boundary for tipping. Noisy trajectories will tend to cycle around the periodic orbit as the noise vanishes, but as the noise becomes slightly larger, the escaping paths become resistant to cycling. An interesting phenomena exposed is that a subset of the unstable manifold of the fixed point in the Euler-Lagrange system, with Maslov index zero, determines where the noisy trajectories escape. After considering tipping mechanisms individually, we consider a one-dimensional differential equation with both additive noise and a ramp parameter. The addition of noise to the system can cause it to tip well below the critical rate at which rate-induced tipping would occur. We achieve this by finding a global minimizer of the Freidlin-Wentzell functional of large deviation theory that represents the most probable path for tipping. This is realized as a heteroclinic connection for the Euler-Lagrange system associated with the Freidlin-Wentzell action and it exists for all rates less than or equal to the critical rate. This framework is extended to show the existence of a heteroclinic orbit for a fairly general class of functions.Doctor of Philosoph

A Dynamical Systems Approach for Most Probable Escape Paths over Periodic Boundaries

Analyzing when noisy trajectories, in the two dimensional plane, of a stochastic dynamical system exit the basin of attraction of a fixed point is specifically challenging when a periodic orbit forms the boundary of the basin of attraction. Our contention is that there is a distinguished Most Probable Escape Path (MPEP) crossing the periodic orbit which acts as a guide for noisy escaping paths in the case of small noise slightly away from the limit of vanishing noise. It is well known that, before exiting, noisy trajectories will tend to cycle around the periodic orbit as the noise vanishes, but we observe that the escaping paths are stubbornly resistant to cycling as soon as the noise becomes at all significant. Using a geometric dynamical systems approach, we isolate a subset of the unstable manifold of the fixed point in the Euler-Lagrange system, which we call the River. Using the Maslov index we identify a subset of the River which is comprised of local minimizers. The Onsager-Machlup (OM) functional, which is treated as a perturbation of the Friedlin-Wentzell functional, provides a selection mechanism to pick out a specific MPEP. Much of the paper is focused on the system obtained by reversing the van der Pol Equations in time (so-called IVDP). Through Monte-Carlo simulations, we show that the prediction provided by OM-selected MPEP matches closely the escape hatch chosen by noisy trajectories at a certain level of small noise.Comment: 28 pages, 15 figure

Tipping in a Low-Dimensional Model of a Tropical Cyclone

A presumed impact of global climate change is the increase in frequency and intensity of tropical cyclones. Due to the possible destruction that occurs when tropical cyclones make landfall, understanding their formation should be of mass interest. In 2017, Kerry Emanuel modeled tropical cyclone formation by developing a low-dimensional dynamical system which couples tangential wind speed of the eye-wall with the inner-core moisture. For physically relevant parameters, this dynamical system always contains three fixed points: a stable fixed point at the origin corresponding to a non-storm state, an additional asymptotically stable fixed point corresponding to a stable storm state, and a saddle corresponding to an unstable storm state. The goal of this work is to provide insight into the underlying mechanisms that govern the formation and suppression of tropical cyclones through both analytical arguments and numerical experiments. We present a case study of both rate and noise-induced tipping between the stable states, relating to the destabilization or formation of a tropical cyclone. While the stochastic system exhibits transitions both to and from the non-storm state, noise-induced tipping is more likely to form a storm, whereas rate-induced tipping is more likely to be the way a storm is destabilized, and in fact, rate-induced tipping can never lead to the formation of a storm when acting alone. For rate-induced tipping acting as a destabilizer of the storm, a striking result is that both wind shear and maximal potential velocity have to increase, at a substantial rate, in order to effect tipping away from the active hurricane state. For storm formation through noise-induced tipping, we identify a specific direction along which the non-storm state is most likely to get activated

ORCID Author Identifiers: A Primer for Librarians

The ORCID (Open Researcher and Contributor ID) registry helps disambiguate authors and streamline research workflows by assigning unique 16-digit author identifiers that enable automatic linkages between researchers and their scholarly activities. This article describes how ORCID works, the benefits of using ORCID, and how librarians can promote ORCID at their institutions by raising awareness of ORCID, helping researchers create and populate ORCID profiles, and integrating ORCID identifiers into institutional repositories and other university research information systems