Localized breather with perturbations in a noisy trap

Perturbations (rand=white noise in [0.5:0.5]):
widths: c = c + pert*c*rand
heights: A = A + pert*A*rand
phases: d = d + pert*d*rand
velocities: vel = vel + pert*vel*rand
positions: xi = xi + pert*xi*rand

potential: V = V + 0.1*pert*V*rand (once at the beginning only)
noise: u = u + noise*u*rand (EVERY iteration)

Different runs:


Breather with factor=1.65, factor0=1.3:
steady state: noise=1e-5, pert=0.1
breather: noise=0, pert=0.00, nocutoff
breather: noise=0, pert=0.00
breather: noise=0, pert=0.10 on V(x) only
breather: noise=1e-5, pert=0.05, nocutoff
breather: noise=1e-5, pert=0.10
breather: noise=1e-6, pert=0.01
breather: noise=1e-6, pert=0.05
breather: noise=1e-6, pert=0.05, nocutoff
breather: noise=1e-6, pert=0.10
breather: noise=1e-7, pert=0.05
Breather found from homoclinic ornit R=9, V0=0.025, lp=1.9325546, w=0.11450412
breather: noise=0, pert=0.00, nocutoff
breather: noise=5, pert=0.05, cutoff=1
breather: noise=5, pert=0.10, cutoff=1