K
Kathleen A. Hoffman
Researcher at University of Maryland, Baltimore County
Publications - 29
Citations - 703
Kathleen A. Hoffman is an academic researcher from University of Maryland, Baltimore County. The author has contributed to research in topics: Central pattern generator & Boundary value problem. The author has an hindex of 14, co-authored 26 publications receiving 637 citations. Previous affiliations of Kathleen A. Hoffman include University of Maryland, Baltimore.
Papers
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The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations ∗
TL;DR: A hybrid system consisting of the dynamics of the trajectories on the slow manifold coupled with "jumps" at the folds in the critical manifold to approximate the fast subsystem leads to an understanding of the bifurcations in the periodic orbits of the forced van der Pol system.
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Numerical computation of canards
TL;DR: This work presents an example of a singularly perturbed system of ordinary differential equations that arises as a model of the electrical potential across the cell membrane of a neuron that was numerically computed using continuation of solutions of boundary value problems.
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The Forced van der Pol Equation II: Canards in the Reduced System ∗
Katherine A. Bold,Chantal Edwards,John Guckenheimer,Sabyasachi Guharay,Kathleen A. Hoffman,Judith Hubbard,Ricardo Oliva,Warren Weckesser +7 more
TL;DR: This paper extends the reduced system to account for canards, trajectory segments that follow the unstable portion of the slow manifold in the forced van der Pol oscillator, and concludes with computations of return maps and periodic orbits in the full three dimensional flow that are compared with the computations and analysis of the reduction system.
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Period Doubling Cascades in a Predator-Prey Model with a Scavenger
TL;DR: A scavenger species that scavenges the predator and is also a predator of the common prey is introduced, analytically proving that all trajectories are bounded in forward time, and numerically demonstrating persistent bounded paired cascades of period-doubling orbits over a wide range of parameter values.
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Bifurcations of relaxation oscillations near folded saddles
TL;DR: This paper investigates the bifurcations that are associated with one type of degeneracy that occurs in systems with two slow variables, in which relaxation oscillations become homoclinic to a folded saddle.