¹û¶³´«Ã½

Alanna Hoyer-Leitzel is an applied dynamist, whose research focuses on disturbance, tipping and bifurcations in dynamical systems, with applications in physics, ecology, and biology. Motivated by the concept of disturbance and recovery in resilience, she works with a type of impulsive differential equation called a "flow-kick system" where disturbances occur on a time scale that is much quicker, if not instantaneous, compared to the time scale of the underlying system's recovery. Hoyer-Leitzel and collaborators have applied this type of model to harvesting in fisheries, meltwater pulses in ocean currents, nutrient runoff in lakes, fires in savannas, and viral re-exposure in the human immune system. Recently, she has been working to expand this modeling framework to stochastic dynamics.

Hoyer-Leitzel's original interest in dynamical systems started in Hamiltonian n-point problems, specifically relative equilibria in the n-body and n-vortex problem. In the limiting case of one large and n infinitesimal vortices, she has classified all symmetric relative equilibria with three infinitesimal vortices and all symmetric relative equilibria with four infinitesimal vortices that have one degree of spatial freedom.