Katherine Meyer
Carleton College, MN·Mathematics & Statistics
Fires, hurricanes and other repeated shocks keep pushing ecosystems away from their usual state, yet most mathematical measures of resilience assume a system sits near a steady state. Resilience is widely discussed in environmental science, but its meaning is often left vague or disputed.
- Fields
Mathematics & Statistics
Ecology & Evolution
- Topics
dynamical systems
resilience
disturbance ecology
- Grants
- 1 known grant, through Aug 2027
What they work on
- Generalize the "intensity" measure of resilience from attractors to repellers and then to Morse sets, working with Conley theory experts to quantify how vulnerable different dynamic structures are to disturbance.
- Determine when ordinary differential equation (ODE) models capture the rough behavior of flow-kick systems, in which continuous recovery is punctuated by periodic discrete disturbances.
- Test the conjecture that periodic orbits and Hopf bifurcations in an ODE model carry over to nearby flow-kick models that have the same average disturbance rate.
More about the research
Dynamical systems, the branch of mathematics that studies how systems change over time, offers a common language for making it precise. This project develops that theory for systems that face ongoing disturbance and never settle down.
Why it matters
This is mainly basic mathematics. It gives ecologists and environmental scientists sharper, formally defined tools for describing resilience when ecosystems face repeated disturbances such as fires and hurricanes. Clarifying when simple differential-equation models are good enough could inform how scientists choose models for disturbed ecosystems.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Chongchun Zeng
Georgia Institute of Technology, GA·Mathematics & Statistics
Analyze two-dimensional water waves linearized at shear flows, where speed varies with depth, establishing the bifurcation of instability and linear inviscid damping for gravity water waves.
Paul Carter
University of California-Irvine, CA·Mathematics & Statistics·Early-career
Analyze when bistable planar interfaces, boundaries between two stable states, become unstable and form patterns in multi-component reaction-diffusion systems, motivated by desertification fronts in drylands.
Jason Mireles-James
Florida Atlantic University, FL·Mathematics & Statistics
Extend high-order computational methods for hyperbolic invariant objects to the parabolic case, where nearby trajectories separate slowly, in Hamiltonian systems.
The school
Carleton College: 4 labs on PI Pages, $5M a year on research.
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