A Fast Eulerian Approach for Computation of Global Isochrons in High Dimensions

作者：Detrixhe Miles^*; Doubeck Marion; Moehlis Jeff; Gibou Frederic

来源：SIAM Journal on Applied Dynamical Systems, 2016, 15(3): 1501-1527.

DOI：10.1137/140998615

• isochrons
• neuron models
• mixed mode oscillation (MMO)
• desynchronization
• Hamilton-Jacobi
• parallel
• high dimensions

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.

• 出版日期2016