[Date Index]
[Thread Index]
[Author Index]
Coupled Map Lattice (Pls. Check the Mathematica Code and advice)
*To*: mathgroup at smc.vnet.net
*Subject*: [mg81339] Coupled Map Lattice (Pls. Check the Mathematica Code and advice)
*From*: B^3 <bbbld at rediffmail.com>
*Date*: Wed, 19 Sep 2007 05:40:25 -0400 (EDT)
I am trying a code as per Mathematuca Guide for Graphics.. but not
sure wheter it will work or not.. even for low range/iterations it
takes tooo long time.................. (the problem is given at the
end).
Here goes the code:
Module[{rang = 500, k = 0.9, omega = 0.068, epsilon = 0.3, incr = 0.2},
step[l_, epsilon_, f_] := (1 - epsilon)f(l) + (epsilon/2)
(f[RotateRight[l]] + f[RotateLeft[l]]);
f = FractionalPart[# - k/(2Pi)Sin[2Pi#] + omega] &;
lembda = Abs[Sin[7^(1/7)Range[rang]]];
tabul = Table[lembda = step[lembda, epsilon, f];
{#, j} & /@ Flatten[Position[Abs[Subtract @@@ Partition[lembda, 2,
1]], _?(# > incr &)]], {j,rang}];
Show[Graphics[Map[Rectangle[# - .5, # + .5] &, tabul, {2}]],
AspectRatio -> Automatic]]
The Problem:
We have a continuous variable x_i(t) at each site i at time t where
1<=i<=N. The evolution of x_i(t) is defined by
x_i(t+1) = F[x_i(t)] - (epsilon/2)[x_(i-1)(t) +x_(i+1)(t) - 2x_i(t)]
The parameter 'epsilon' is the coupling strength and the function
F(x)
is the circle map
F(x)= x + omega -(k/2*Pi)sin(2*Pi*x)
The dynamics is confined to the interval [0,1] using
If int[x_i(t)]=m, x_i(t)=x_i(t)-m if x_i(t) >0
x_i(t)=x_i(t)-m+1 if x_i(t)<0
The fixed point solution of for the local map F(x) is given by
x* = (1/2*Pi) sin(-1)(2*Pi*omega/k)
My Problem is to draw "Space-Time" plot for the system, for say
omega=0.068, epsilon=0.3, k=0.9, N=500.
Prev by Date:
**V6 Help Browser**
Next by Date:
**confusion about Mathematica Print, Messages, Console, Stdout, Stderr and all that.**
Previous by thread:
**V6 Help Browser**
Next by thread:
**confusion about Mathematica Print, Messages, Console, Stdout, Stderr and all that.**
| |