29 citations · 52 across the 16 of their papers we have counts for
5 papers · 1 filter
Phase Response Curves and the Role of Coordinates
Simon Wilshin, Matthew D. Kvalheim, Shai Revzen
The "Phase Response Curve" (PRC) is a common tool used to analyze phase resetting in the natural sciences. We make the observation that the PRC with respect to a coordinate $y\in\m…
A pasting lemma for Lipschitz functions
Matthew D. Kvalheim, Paul Gustafson, Samuel A. Burden
We give a necessary and sufficient condition ensuring that any function which is separately Lipschitz on two fixed compact sets is Lipschitz on their union.
Poincaré-Hopf theorem for hybrid systems
Matthew D. Kvalheim
A generalization of the Poincaré-Hopf index theorem applicable to hybrid dynamical systems is obtained. For the hybrid systems considered, guard sets are not assumed to be smooth;…
Flux in tilted potential systems: negative resistance and persistence
Yuliy Baryshnikov, Matthew D. Kvalheim
Many real-world systems are well-modeled by Brownian particles subject to gradient dynamics plus noise arising, e.g., from the thermal fluctuations of a heat bath. Of central impor…
Necessary conditions for feedback stabilization and safety
Matthew D. Kvalheim, Daniel E. Koditschek
Brockett's necessary condition yields a test to determine whether a system can be made to stabilize about some operating point via continuous, purely state-dependent feedback. For…