I have a problem integrating the 'standard map' (
http://en.wikipedia.org/wiki/Standard_map
http://en.wikipedia.org/wiki/Standard_map ) with deSolve:
By using the modulo-operator '%%' with 2*pi in the ODEs (standardmap1), the
resulting values of P and Theta, should not be greater than 2pi. Because
this was not the case, i was thinking that the function 'ode' has some
internal problems with the '%%' or integrating periodical ODEs, so I wrote a
modulo-function by myself (modulo and standardmap2). But still I get values
much higher than 2pi and I cannot find the error... Any guess?
Thanks
Full code:
----------------------------------------------------------------
library(deSolve)
iterations <- 100
Parameter <- c(k = 0.6)
State <- c(Theta = 1 , P = 1)
Time <- 0:iterations/10
standardmap1 <- function(Time, State, Parameter){
with(as.list(c(State, Parameter)), {
dP <- (P + k * sin(Theta)) %% (2 * pi)
dTheta <- (P + Theta) %% (2 * pi)
return(list(c(dP, dTheta)))
})
}
#solve ode using standardmap1
out1 <- as.data.frame(ode(func = standardmap1, y = State,parms = Parameter,
times = Time))
# x mod y, end: maximal iterations
modulo <- function(x,y,end=1000){
for (n in 0:end)
if (x > (n-1)*y)
z = x - (n-1)*y
if (z > 0)
return(z)
else break
}
standardmap2 <- function(Time, State, Parameter){
with(as.list(c(State, Parameter)), {
dTheta <- modulo((P + Theta),(2*pi))
dP <- modulo(P + k *sin(Theta),(2*pi))
return(list(c(dP, dTheta)))
})
}
#solve ode using standardmap2
out2 <- as.data.frame(ode(func = standardmap2, y = State,parms = Parameter,
times = Time))
#plot the results
matplot(out1[2],out1[3], type = "p", pch = ".")
matplot(out2[2],out2[3], type = "p", pch = ".")
--
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