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RCsin2_dde_biff.py
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RCsin2_dde_biff.py
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import numpy as np
import pylab as pl
from math import sin
from pydelay import dde23
# define the equations
eqns = {
'x' : '(1/tau) *(-x-y+beta*pow(sin(sc*(0.05967*x(t-0.0067*T)+\
0.68260*x(t-0.0133*T)+\
0.04247*x(t-0.0200*T)+\
0.07151*x(t-0.0267*T)+\
0.52213*x(t-0.0333*T)+\
0.09682*x(t-0.0400*T)+\
0.81890*x(t-0.0467*T)+\
0.81830*x(t-0.0533*T)+\
0.72310*x(t-0.0600*T)+\
0.15000*x(t-0.0667*T)+\
0.66021*x(t-0.0733*T)+\
0.51907*x(t-0.0800*T)+\
0.97387*x(t-0.0867*T)+\
0.64959*x(t-0.0933*T)+\
0.80107*x(t-0.1000*T)+\
0.45422*x(t-0.1067*T)+\
0.43279*x(t-0.1133*T)+\
0.82607*x(t-0.1200*T)+\
0.08355*x(t-0.1267*T)+\
0.13329*x(t-0.1333*T)+\
0.17355*x(t-0.1400*T)+\
0.39130*x(t-0.1467*T)+\
0.83214*x(t-0.1533*T)+\
0.80410*x(t-0.1600*T)+\
0.06053*x(t-0.1667*T)+\
0.39963*x(t-0.1733*T)+\
0.52736*x(t-0.1800*T)+\
0.41718*x(t-0.1867*T)+\
0.65746*x(t-0.1933*T)+\
0.62855*x(t-0.2000*T)+\
0.29225*x(t-0.2067*T)+\
0.43205*x(t-0.2133*T)+\
0.01550*x(t-0.2200*T)+\
0.98497*x(t-0.2267*T)+\
0.16732*x(t-0.2333*T)+\
0.10631*x(t-0.2400*T)+\
0.37275*x(t-0.2467*T)+\
0.19830*x(t-0.2533*T)+\
0.49014*x(t-0.2600*T)+\
0.33981*x(t-0.2667*T)+\
0.95251*x(t-0.2733*T)+\
0.92118*x(t-0.2800*T)+\
0.05273*x(t-0.2867*T)+\
0.73854*x(t-0.2933*T)+\
0.26937*x(t-0.3000*T)+\
0.42322*x(t-0.3067*T)+\
0.54838*x(t-0.3133*T)+\
0.94360*x(t-0.3200*T)+\
0.41813*x(t-0.3267*T)+\
0.98396*x(t-0.3333*T)+\
0.30173*x(t-0.3400*T)+\
0.70174*x(t-0.3467*T)+\
0.66695*x(t-0.3533*T)+\
0.53962*x(t-0.3600*T)+\
0.69875*x(t-0.3667*T)+\
0.66714*x(t-0.3733*T)+\
0.17830*x(t-0.3800*T)+\
0.12813*x(t-0.3867*T)+\
1.00000*x(t-0.3933*T)+\
0.17128*x(t-0.4000*T)+\
0.03263*x(t-0.4067*T)+\
0.56172*x(t-0.4133*T)+\
0.88268*x(t-0.4200*T)+\
0.66979*x(t-0.4267*T)+\
0.19061*x(t-0.4333*T)+\
0.36926*x(t-0.4400*T)+\
0.46115*x(t-0.4467*T)+\
0.98254*x(t-0.4533*T)+\
0.15655*x(t-0.4600*T)+\
0.85631*x(t-0.4667*T)+\
0.64536*x(t-0.4733*T)+\
0.37662*x(t-0.4800*T)+\
0.19110*x(t-0.4867*T)+\
0.42865*x(t-0.4933*T)+\
0.48247*x(t-0.5000*T)+\
0.12072*x(t-0.5067*T)+\
0.59005*x(t-0.5133*T)+\
0.22640*x(t-0.5200*T)+\
0.38497*x(t-0.5267*T)+\
0.58352*x(t-0.5333*T)+\
0.25204*x(t-0.5400*T)+\
0.29071*x(t-0.5467*T)+\
0.61766*x(t-0.5533*T)+\
0.26553*x(t-0.5600*T)+\
0.82514*x(t-0.5667*T)+\
0.98357*x(t-0.5733*T)+\
0.73092*x(t-0.5800*T)+\
0.34419*x(t-0.5867*T)+\
0.58461*x(t-0.5933*T)+\
0.10787*x(t-0.6000*T)+\
0.90714*x(t-0.6067*T)+\
0.88046*x(t-0.6133*T)+\
0.81851*x(t-0.6200*T)+\
0.26097*x(t-0.6267*T)+\
0.59490*x(t-0.6333*T)+\
0.02253*x(t-0.6400*T)+\
0.42565*x(t-0.6467*T)+\
0.31301*x(t-0.6533*T)+\
0.16163*x(t-0.6600*T)+\
0.17893*x(t-0.6667*T)+\
0.42327*x(t-0.6733*T)+\
0.09432*x(t-0.6800*T)+\
0.59907*x(t-0.6867*T)+\
0.47136*x(t-0.6933*T)+\
0.69659*x(t-0.7000*T)+\
0.70053*x(t-0.7067*T)+\
0.63912*x(t-0.7133*T)+\
0.03363*x(t-0.7200*T)+\
0.06887*x(t-0.7267*T)+\
0.31989*x(t-0.7333*T)+\
0.53135*x(t-0.7400*T)+\
0.65505*x(t-0.7467*T)+\
0.40799*x(t-0.7533*T)+\
0.82074*x(t-0.7600*T)+\
0.71902*x(t-0.7667*T)+\
0.96954*x(t-0.7733*T)+\
0.53182*x(t-0.7800*T)+\
0.32544*x(t-0.7867*T)+\
0.10573*x(t-0.7933*T)+\
0.61152*x(t-0.8000*T)+\
0.77952*x(t-0.8067*T)+\
0.42384*x(t-0.8133*T)+\
0.09091*x(t-0.8200*T)+\
0.26672*x(t-0.8267*T)+\
0.15380*x(t-0.8333*T)+\
0.28126*x(t-0.8400*T)+\
0.44049*x(t-0.8467*T)+\
0.52763*x(t-0.8533*T)+\
0.45785*x(t-0.8600*T)+\
0.87618*x(t-0.8667*T)+\
0.51853*x(t-0.8733*T)+\
0.94449*x(t-0.8800*T)+\
0.63830*x(t-0.8867*T)+\
0.95858*x(t-0.8933*T)+\
0.24093*x(t-0.9000*T)+\
0.67674*x(t-0.9067*T)+\
0.28933*x(t-0.9133*T)+\
0.67243*x(t-0.9200*T)+\
0.69578*x(t-0.9267*T)+\
0.06806*x(t-0.9333*T)+\
0.25502*x(t-0.9400*T)+\
0.22425*x(t-0.9467*T)+\
0.66845*x(t-0.9533*T)+\
0.84517*x(t-0.9600*T)+\
0.34478*x(t-0.9667*T)+\
0.78124*x(t-0.9733*T)+\
0.67595*x(t-0.9800*T)+\
0.00672*x(t-0.9867*T)+\
0.60272*x(t-0.9933*T)+\
0.38713*x(t-1.0000*T))+Phi0),2)-\
beta*pow(sin(Phi0),2))',
'y' : '(1/theta)*x'
}
bn=0.5;
bf=10.5;
bsteps=5;
hb=(bf-bn)/bsteps;
#define the parameters, times is in 'ms'
params = {
'tau' : 0.09, # 0.008 ms < tau< 0.10 ms
'beta' : bn,
'T' : 10.5, # 1.6 ms < T< 130 ms
'Phi0' : 0.25*np.pi,
'theta' : 543.0, # 0.8 ms < theta< 1*1000 ms
'sc' : 1/72.3924
}
#print(params)
# set the history of to the constant function 0.5 (using a python lambda function)
histfunc = {
'x': lambda t: 0.2*sin(0.2*t),
'y': lambda t: 0.000003452
}
#output diagramm
hbin=300;
Hist=np.zeros((bsteps+1,hbin));
Hdwn=-2.0;
Hup=2.0;
for k in range(1,bsteps+2):
params['beta']=bn+(k-1)*hb
# Initialise the solver
dde = dde23(eqns=eqns, params=params)
#set the simulation parameters
# (solve from t=0 to t=tfinal and limit the maximum step size to dtmax)
tfinal=18000
tcut=7000
dde.set_sim_params(tfinal=tfinal, dtmax=0.5, AbsTol=10**-6, RelTol=10**-3)
# set the history
dde.hist_from_funcs(histfunc, 100)
# run the simulator
dde.run()
x = dde.sol['x']
t = dde.sol['t']
H, xedges = np.histogram(x[np.ceil(len(x)*0.6):], bins=hbin, range=(Hdwn,Hup))
Hist[k-1,:]=H.astype(float)/max(H.astype(float))
#Show picture
T=params['T']
#beta=params['beta']
tau=params['tau']
theta=params['theta']
pl.imshow(np.transpose(Hist), extent=(bn,bf,Hdwn,Hup))
pl.axis('tight')
pl.title(r'$\theta=$ %1.2f, $\tau=$ %1.2f, T= %1.2f'
% (theta, tau, T ) )
pl.xlabel(r'$\beta$')
pl.ylabel('$x(t)$')
pl.show()