Matlab code to reproduce computations in [Carter, de Rijk, and Sandstede 2016].
This repository provides Matlab code to reproduce the numerical results presented in Figures 6 and 7 in P Carter, B de Rijk, and B Sandstede. Stability of traveling pulses with oscillatory tails in the FitzHugh-Nagumo system. Journal of Nonlinear Science 26 (2016) 1369–1444. Details about the methods can be found in this paper.
The code consists of three Matlab scripts:
solve_FHN_w.m finds pulses with monotone and oscillatory puldses for the traveling-wave equation of the FitzHugh-Nagumo system and computes the critical eigenfunction of the weighted eigenvalue problem. Users can select the parameters and initial guesses in lines 33-58 of this script and run this script in Matlab to reproduce the results in the paper cited above.
FHNeqn_w_periodic.m is an auxiliary script that returns the right-hand side of the FHN equation and the (weighted) Jacobian
fourdif.m provides Fourier differentiation matrices
The initial data for the three different computations are contained in the Matlab data files initial_pulse_{1,2,3}.mat.