                                                                                 .txt
***    MDIM   LTAU  
***               1-4    
*** : TAU(i) , ALFA(j), GAMA(j),TETA(j), B(i,j, k),
***             i=1,2,..,LTAU, j = 1,2,..,MDIM, k = 1,2,..,MDIM                     
*********************************************************************************************

***  1
 :  k=1,2,...,MDIM,

dx(k)/dt = ALFA(k)/[1 + R(k)] - TETA(k)*x(k),

           
                R(k) = S(1) + S(2) +...+S(LTAU)

S(1)    = Z(1)^GAMA(1) + Z(2)^GAMA(2) +...+ Z(MDIM)^GAMA(MDIM)
                Z(j) = x(j)(t-TAU(1))/BETA(1,j,k)
S(2)    = Z(1)^GAMA(1) + Z(2)^GAMA(2) +...+ Z(MDIM)^GAMA(MDIM)
                Z(j) = x(j)(t-TAU(2))/BETA(2,j,k)
...........................................................
S(LTAU) = Z(1)^GAMA(1) + Z(2)^GAMA(2) +...+ Z(MDIM)^GAMA(MDIM)
               Z(j) = x(j)(t-TAU(LTAU))/BETA(LTAU,j,k)

***  2
 :  k=1,2,...,MDIM,

dx(k)/dt = ALFA(k)/R(k) - TETA(k)*x(k),

           
            R(k) = [1+S(1)]*[1+ S(2)]*...*[1+S(LTAU)]

S(1)    = Z(1)^GAMA(1) + Z(2)^GAMA(2) +...+ Z(MDIM)^GAMA(MDIM)
                Z(j) = x(j)(t-TAU(1))/BETA(1,j,k)
S(2)    = Z(1)^GAMA(1) + Z(2)^GAMA(2) +...+ Z(MDIM)^GAMA(MDIM)
                Z(j) = x(j)(t-TAU(2))/BETA(2,j,k)
...........................................................
S(LTAU) = Z(1)^GAMA(1) + Z(2)^GAMA(2) +...+ Z(MDIM)^GAMA(MDIM)
               Z(j) = x(j)(t-TAU(LTAU))/BETA(LTAU,j,k)

***  3
 :  k=1,2,...,MDIM,

dx(k)/dt = ALFA(k)/[1 + R(k)] - TETA(k)*x(k),

           
                   R(k) = S(1)*S(2)*...*S(LTAU)

S(1)    = Z(1)^GAMA(1)*Z(2)^GAMA(2)*...*Z(MDIM)^GAMA(MDIM)
                Z(j) = x(j)(t-TAU(1))/BETA(1,j,k)
S(2)    = Z(1)^GAMA(1)*Z(2)^GAMA(2)*...*Z(MDIM)^GAMA(MDIM)
                Z(j) = x(j)(t-TAU(2))/BETA(2,j,k)
...........................................................
S(LTAU) = Z(1)^GAMA(1)*Z(2)^GAMA(2)*...*Z(MDIM)^GAMA(MDIM)
               Z(j) = x(j)(t-TAU(LTAU))/BETA(LTAU,j,k)

***  4
 :  k=1,2,...,MDIM,

dx(k)/dt = ALFA(k)*R(k) - TETA(k)*x(k),

           
                 R(k) = S(1) + S(2) +...+ S(LTAU)

S(1)    = Z(1)^GAMA(1) + Z(2)^GAMA(2) +...+ Z(MDIM)^GAMA(MDIM)
               Z(j) = 1/[1+x(j)(t-TAU(1))/BETA(1,j,k)]
S(2)    = Z(1)^GAMA(1)*Z(2)^GAMA(2)*...*Z(MDIM)^GAMA(MDIM)
               Z(j) = 1/[1+x(j)(t-TAU(2))/BETA(2,j,k)]
...........................................................
S(LTAU) = Z(1)^GAMA(1)*Z(2)^GAMA(2)*...*Z(MDIM)^GAMA(MDIM)
               Z(j) = 1/[1+x(j)(t-TAU(LTAU))/BETA(LTAU,j,k)]

     t    
 x(k).       
 BETA(i,j,k)  BETA

******************************************************************************************    
  


