Characterizing tipping events in piecewise-smooth systems

WAKE FOREST UNIVERSITY
DEPARTMENT OF MATHEMATICS & STATISTICS

Presents

Kaitlin Hill
Wake Forest University

Thursday, April 2nd, 2020
11am
Virtual Colloquium via Zoom
Meeting details will be available in department newsletter

Abstract: A system of differential equations is said to ‘tip’ when the state makes a sudden, and possibly extreme, transition from the current state to an alternate state. In deterministic systems, tipping may be induced by phenomena like a bifurcation, or the rate at which a parameter is varied. In stochastic systems, the effect of noise may cause the system to transition from one metastable state to another metastable state as a rare event. In both stochastic and deterministic systems, these types of tipping events are not well-understood when the underlying flow is piecewise-smooth. In particular, we are motivated by models of Arctic energy balance, which typically have a piecewise-smooth geometry, and possible characterizations of tipping events as Arctic sea ice melts. We will explore mechanisms for the robust characterization of tipping in two case studies of piecewise-smooth differential equations, one deterministic and one stochastic.

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