Name
Abstract | ||
|---|---|---|
AbstractPhase reduction methods have been tremendously useful for understanding the dynamics of nonlinear oscillators,but have been difficult to extend to systems with a stable fixed point, such as an excitable system. Usingthe notion of isostables, which measure the time it takes for a given initial condition in phase space toapproach a stable fixed point, we present a general method for isostable reduction for excitable systems. Wealso devise an adjoint method for calculating infinitesimal isostable response curves, which are analogous toinfinitesimal phase response curves for oscillatory systems. Through isostable reduction, we are able toimplement sophisticated control strategies in a high-dimensional model of cardiac activity for the terminationof alternans, a precursor to cardiac fibrillation. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1137/140952478 | Periodicals |
Keywords | Field | DocType |
phase reduction,excitable media,isostable,alternans,cardiology | Cardiac activity,Media theory,Topology,Nonlinear oscillators,Mathematical analysis,Control theory,Phase space,Phase response,Initial value problem,Fixed point,Infinitesimal,Mathematics | Journal |
Volume | Issue | ISSN |
57 | 2 | 0036-1445 |
Citations | PageRank | References |
4 | 0.49 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dan Wilson | 1 | 17 | 3.15 |
| Jeff Moehlis | 2 | 276 | 34.17 |