/* C program that integrates the chaotic chemical system from

J.L.Hudson & O.E.Rossler:
Chaos in Simple Three- and Four-variable Chemical Systems
in Lecture Notes in Biomathematics 55:
Modelling of Patterns in Space and Time
pp.135-145
eds. W.Jager & J.D.Murray
Springer-Verlag Berlin 1984

To run it 
(1) save this code in a file hudson.c
(2) save easynum library in a file easynum.c
(3) compile it by
$ cc hudson.c -lm
(4) run it by
$ a.out

To see the results type
$ xpplot t ca
$ xpplot t cb
$ xpplot t cc
$ xpplot ca cb
$ xpplot ca cc
$ xpplot cb cc

*/
# include "easynum.c" /* http://staff.vscht.cz/~pokornp/easynum */
/******************************/
void hudson (t,y,p, f,g,J,d)
 real t;
 vector y,p, f,g;
 matrix J;
{
 real 
  k1=0.01, k2=0.02, k3=1.0, k=0.08, k4=0.11, k5=0.0005,

  a=y[0],
  b=y[1],
  c=y[2];

 f[0] = k1-k2*(a-c)-k3*b*a;
 f[1] = k3*a*b-k4*b/(b+k)+k5;
 f[2] = k2*(a-c);
} /* hudsun */
/******************************/
int main ()
{
 real t = 0,Ts = 1;
 vector x,p;
 int i,im=10000,d=3;
 FILE *ft,*fa,*fb,*fc;

 ppopenww (&ft ,"t");
 ppopenww (&fa,"ca");
 ppopenww (&fb,"cb");
 ppopenww (&fc,"cc");

 x[0] = 0.8;
 x[1] = 0.01;
 x[2] = 1.0;

 for (i=0;i<im;i++) {
  integdt (&t,Ts,x,hudson,p,d);
  (void) fprintf (ft,"%.12G\n",t);
  (void) fprintf (fa,"%.12G\n",x[0]);
  (void) fprintf (fb,"%.12G\n",x[1]);
  (void) fprintf (fc,"%.12G\n",x[2]);
 };
 return (0);
} /* main */
/*******************************************/