Hello all -
This code will run, but it bogs down my computer when I run it for finer and
finer time increments and more generations. I was wondering if there is a
better way to write my loops so that this wouldn't happen. Thanks!
-Tyler
#################
# Bifurcation diagram
# Using Braaksma system of equations
# We have however used a Fourier analysis
# to get a forcing function similar to
# cardiac action potential...
#################
require(odesolve)
# We get this s_of_t function from Maple ws
s_of_t = function(t)
{
(1/10) * (( (1/2) + (1/2) * (sin((1/4)*pi*t))/(abs(sin((1/4)*pi*t)))) * (
6.588315815*sin((1/4)*pi*t) - 1.697435362*sin((1/2)*pi*t) - 1.570296922*sin
((3/4)*pi*t) + 0.3247901958*sin(pi*t) + 0.7962749105*sin((5/4)*pi*t) +
0.07812230515*sin((3/2)*pi*t) - 0.3424877143*sin((7/4)*pi*t) - 0.1148306748*
sin(2*pi*t) + 0.1063696962*sin((9/4)*pi*t) + 0.02812403009*sin((5/2)*pi*t)))
}
ModBraaksma = function(t, n, p)
{
dx.dt = (1/0.01)*(n[2]-((1/2)*n[1]^2+(1/3)*n[1]^3))
dy.dt = -(n[1]+p["alpha"]) + 0.032 * s_of_t(t)
list(c(dx.dt, dy.dt))
}
initial.values = c(0.1, -0.02)
alphamin = 0.01
alphamax = 0.02
alphas = seq(alphamin, alphamax, by = 0.00001)
TimeInterval = 100
times = seq(0.001, TimeInterval, by = 0.001)
plot(1, xlim = c(alphamin, alphamax), ylim = c(0,0.3), type = "n",xlab
= "Values
of alpha", ylab = "Approximate loop size for a limit cycle", main =
"Bifurcation
Diagram")
for (i in 1:length(alphas)){
params = c(alpha=alphas[i])
out = lsoda(initial.values, times, ModBraaksma, params)
X = out[,2]
Y = out[,3]
for(j in 200:length(times)){
if (abs(X[j]) < 0.001) {
points(alphas[i], Y[j], pch = ".")
}
}
}
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