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coupled map lattice problem

• To: mathgroup at smc.vnet.net
• Subject: [mg81272] coupled map lattice problem
• From: B^3 <bbbld at rediffmail.com>
• Date: Tue, 18 Sep 2007 00:39:52 -0400 (EDT)

It is a coupled map lattice 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.

Please advice me..

• Follow-Ups:
  • Re: coupled map lattice problem
    • From: Daniel Lichtblau <danl@wolfram.com>