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MathGroup Archive 2000

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Lorenz system

  • To: mathgroup at smc.vnet.net
  • Subject: [mg23808] Lorenz system
  • From: Winston Garira <uceswga at ucl.ac.uk>
  • Date: Sat, 10 Jun 2000 03:00:16 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

Can someone help me. I am trying to solve a system of 48 Lorenz
equations which are diffusively coupled. In the system of equations,
k1, k2, and k3 are the coupling strengths (constants) which in this
case I gave the values k1=15.6, k2=8.8 and k3=5.9. In the system a, b,
and c are also constants and I assigned them values a=10, b=27, and
c=8/3. I used initial conditions x[0]=0.7, y[0]=0.3 and z[0]=-1.5. N
(is integer) represents the N th lorenz system and so it has values
from 0 to 48.  In the notebook below in which I tried to plot the N=21
Lorenz system I just got the error that x[t][21], y[t][21], z[t][21]
are not real numbers.

Thank you


Winston



Lorenzs[init1_, init2_, init3_ ,N_, time_, k1_, k2_, k3_, {a_, b_, c_}]:=
Module[{},
     {N,0,48} ;
  lorenz=NDSolve[{
	  x'[t][N]+a*(y[t][N]-x[t][N])+ d1*(x[t][N-1]-2 x[t][N] + x[t][N])==0,
	  y'[t][N]+b*x[t][N]-y[t][N]-x[t][N] y[t][N] + d2*(y[t][N-1]-2 y[t][N]+y[t][N+1])==0,
	  z'[t][N]-c*z[t][N] +z[t][N] y[t][N] + d3 *(z[t][N-1]-2 z[t][N]+z[t][N+1])==0,
  x[0][N]==init1[[1]],
  y[0][N]==init2[[2]],
  z[0][N]==init3[[3]]},
  {x[N], y[N], z[N]},
  {t,0,time}, MaxSteps->200000];
  x[t_][N] := Evaluate[x[t][N] /. lorenz];
  y[t_][N]:= Evaluate[y[t][N] /. lorenz];
  z[t_][N] := Evaluate[z[t][N] /. lorenz];
	]; 

  a=10; b=27; c=8/3;    

  Lorenzs[{0.7,0.3,-1.5}, N, 5000, 15.6, 8.8, 5.9, {a,b,c}];
  Plot[{x[t][21], y[t][21], z[t][21]}, {t,0,600},
  PlotStyle\[Rule]{RGBColor[1,0,0.3],RGBColor[0,0.5,1],RGBColor[1,0,0.3]}];
  
  
  
  



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