Science > Physics > Nonlinear Physics, Coupled Map Lattice, Circular Maps
| Topic: |
Science > Physics |
| User: |
"B^3" |
| Date: |
18 Sep 2007 06:57:44 AM |
| Object: |
Nonlinear Physics, Coupled Map Lattice, Circular Maps |
Hi,
I am interested in Nonlinear Physics. I am working on the following:
(Calculations on Cupled Map Lattice, circular maps), pls advice me
about it:
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....................
Sincerely,
Bhaskar Bidyut B.
.
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| User: "Androcles" |
|
| Title: Re: Nonlinear Physics, Coupled Map Lattice, Circular Maps |
18 Sep 2007 08:17:47 AM |
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"B^3" <bbbld@rediffmail.com> wrote in message
news:1190116664.910549.308370@r29g2000hsg.googlegroups.com...
: Hi,
: I am interested in Nonlinear Physics. I am working on the following:
: (Calculations on Cupled Map Lattice, circular maps), pls advice me
: about it:
:
: 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....................
My free advice is for you to draw "Space-Time" plot for the system,
for say omega=0.068, epsilon=0.3, k=0.9, N=500 using Google Sketchup
which is also free, and then you can wallow on your non-linear musings
with a linear program.
.
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