19 citations · 27 across the 12 of their papers we have counts for
13 papers · 1 filter
A Heterogeneous FitzHugh-Nagumo Model Exhibiting Local and Regional Dynamics that Mimic Spontaneous Atrial Fibrillation
Alexander Hattoum, Camden Kilton, Martin Mohlenkamp +3
We study two-dimensional networks of FitzHugh-Nagumo oscillators in regimes that mimic cardiac tissue. The networks include small layers of cells that have fast-recovery characteri…
Two dimensional heteroclinic attractor in the generalized Lotka-Volterra system
Valentin S. Afraimovich, Gregory Moses, Todd R. Young
We study a simple dynamical model exhibiting sequential dynamics. We show that in this model there exist sets of parameter values for which a cyclic chain of saddle equilibria, $O_…
Two classes of ODE models with switch-like behavior
Winfried Just, Mason Korb, Ben Elbert +1
In cases where the same real-world system can be modeled both by an ODE system $\bD$ and a Boolean system $\bB$ it is of interest to identify conditions under which the two systems…
Stochastic Stability for Flows with Smooth Invariant Measures
Sergiu Aizicovici, Todd Young
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flo…
Clustering in Cell Cycle Dynamics with General Response/Signaling Feedback
Todd Young, Bastien Fernandez, Richard Buckalew +2
Motivated by experimental and theoretical work on autonomous oscillations in yeast, we analyze ordinary differential equations models of large populations of cells with cell-cycle…
The Hopf bifurcation with bounded noise
Ryan Botts, Ale Jan Homburg, Todd Young
We study Hopf-Andronov bifurcations in a class of random differential equations (RDEs) with bounded noise. We observe that when an ordinary differential equation that undergoes a H…