Name
Abstract | ||
|---|---|---|
We present a novel Eulerian numerical method to compute global isochrons of a stable periodic orbit in high dimensions. Our approach is to formulate the asymptotic phase as a solution to a first order boundary value problem and solve the resulting Hamilton-Jacobi equation with the parallel fast sweeping method. All isochrons are then given as isocontours of the phase. We apply this method to the Hodgkin-Huxley equations and a model of a dopaminergic neuron which exhibits mixed mode oscillations. Our results show that this Eulerian scheme is an efficient, accurate method for computing the asymptotic phase of a periodic dynamical system. Furthermore, by computing the phase on a Cartesian grid, it is simple to compute the gradient of phase, and thus compute an "almost phaseless" target set for the purposes of desynchronization of a system of oscillators. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/140998615 | SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS |
Keywords | Field | DocType |
isochrons,neuron models,mixed mode oscillation (MMO),desynchronization,Hamilton-Jacobi,parallel,high dimensions | Boundary value problem,Oscillation,Regular grid,Mathematical analysis,Eulerian path,Numerical analysis,Periodic graph (geometry),Mathematics,Dynamical system,Computation | Journal |
Volume | Issue | ISSN |
15 | 3 | 1536-0040 |
Citations | PageRank | References |
2 | 0.36 | 11 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Miles Detrixhe | 1 | 23 | 1.72 |
| Marion Doubeck | 2 | 2 | 0.36 |
| Jeff Moehlis | 3 | 276 | 34.17 |
| Frédéric Gibou | 4 | 850 | 64.05 |