format version = 1.0
 
 
 begin problem ss_ethanolferm1                     
 
 type = SSystem
 date =  14-Aug-08 09:53:28
 url = www.odeidentification.org
 
 
 // An S-system has the generic ODE:
 // d/dt X_i = alpha_i * (PRODUCT_j (X_j)^g_ij) - 
 //            beta_i * (PRODUCT_j (X_j)^h_ij)
 // where: alpha is a vector of length n
 //        beta is a vector of length n
 //        g is an n*n matrix
 //        h is an n*n matrix
 //        n is the number of variables
 
 
// VARIABLES
 
 variable_1 has name = x1 is dependent
 variable_2 has name = x2 is dependent
 variable_3 has name = x3 is dependent
 variable_4 has name = x4 is dependent
 
 
// MODEL SPACE
 
 alpha has defaultLowerBound =  0.
 
 alpha has defaultUpperBound =  5.
 
 beta has defaultLowerBound =  0.
 
 beta has defaultUpperBound =  5.
 
 g has defaultLowerBound =  -3.
 
 g has defaultUpperBound =   3.
 
 h has defaultLowerBound =  -3.
 
 h has defaultUpperBound =   3.
 
 
 
 
// ERROR FUNCTION
 
 errorFunction
 has type = minusLogLikelihoodPlusLambdaK
 has equation = -L+lambda*K
 has lambda =   1
 
 
 // EXPERIMENTS
 
 experiment_1 has name = exp1
 experiment_2 has name = exp2
 
 
// EXPERIMENT 1
sample_1 of experiment_1
has time =  0
has variable_ =  0.32138 98.4237 0 0
has sdev of variable_ = 0.017275 0.033446 0.1 0.1
 
sample_2 of experiment_1
has time =  1
has variable_ =  0.55582 96.1842 0 0
has sdev of variable_ = 0.014682 0.58803 0.1 0.1
 
sample_3 of experiment_1
has time =  2
has variable_ =  1.1656 93.1433 0.8453 0
has sdev of variable_ = 0.21828 1.0512 1.1954 0.1
 
sample_4 of experiment_1
has time =  3
has variable_ =  1.9665 89.4814 3.9807 0.2561
has sdev of variable_ = 0.38911 0.16766 1.6769 0.36218
 
sample_5 of experiment_1
has time =  4
has variable_ =  3.1822 81.6356 6.9194 0.3673
has sdev of variable_ = 0.16012 3.9094 3.0902 0.51944
 
sample_6 of experiment_1
has time =  5
has variable_ =  5.4744 69.6836 11.5906 1.0449
has sdev of variable_ = 0.14716 10.6298 5.8449 0.044258
 
sample_7 of experiment_1
has time =  6
has variable_ =  7.594 50.4962 18.4895 1.4041
has sdev of variable_ = 0.40562 15.5617 6.0806 0.020655
 
sample_8 of experiment_1
has time =  7
has variable_ =  10.2692 31.2942 26.995 1.897
has sdev of variable_ = 0.23525 13.4432 5.8734 0.082689
 
sample_9 of experiment_1
has time =  8
has variable_ =  11.1342 15.0058 35.0239 2.4328
has sdev of variable_ = 0.00035355 12.8612 5.8693 0.13836
 
sample_10 of experiment_1
has time =  9
has variable_ =  12.3686 3.8 40.5563 2.7454
has sdev of variable_ = 0.021496 5.374 3.2796 0.28067
 
sample_11 of experiment_1
has time =  10
has variable_ =  12.6412 0 42.9921 2.8563
has sdev of variable_ = 0.24141 0.1 0.38587 0.39056
 
 
 
 
// EXPERIMENT 2
sample_1 of experiment_2
has time =  0
has variable_ =  0.2607 151.241 0 0
has sdev of variable_ = 0.1212 1.755 0.1 0.1
 
sample_2 of experiment_2
has time =  1
has variable_ =  0.3449 150.2995 0 0
has sdev of variable_ = 0.07764 1.8378 0.1 0.1
 
sample_3 of experiment_2
has time =  2
has variable_ =  0.64775 149.389 0 0
has sdev of variable_ = 0.060458 0.55013 0.1 0.1
 
sample_4 of experiment_2
has time =  3
has variable_ =  1.2406 147.1655 1.9422 0.23365
has sdev of variable_ = 0.0077075 1.1802 2.7466 0.33043
 
sample_5 of experiment_2
has time =  4
has variable_ =  1.9698 142.819 4.5141 0.3827
has sdev of variable_ = 0.27881 5.9128 2.8527 0.54122
 
sample_6 of experiment_2
has time =  5
has variable_ =  3.0478 132.7825 7.4811 0.99425
has sdev of variable_ = 0.24438 10.2071 5.0941 0.20541
 
sample_7 of experiment_2
has time =  6
has variable_ =  5.0755 116.6395 13.6387 1.495
has sdev of variable_ = 0.169 11.8235 6.6903 0.3252
 
sample_8 of experiment_2
has time =  7
has variable_ =  7.5743 94.7079 19.0816 1.9185
has sdev of variable_ = 1.5942 18.7979 8.0916 0.40517
 
sample_9 of experiment_2
has time =  8
has variable_ =  8.8361 77.12 26.5594 2.41
has sdev of variable_ = 0.17699 18.6394 8.7871 0.33368
 
sample_10 of experiment_2
has time =  9
has variable_ =  9.7001 61.6384 34.4949 3.0079
has sdev of variable_ = 0.32371 18.6134 9.2997 0.2402
 
sample_11 of experiment_2
has time =  10
has variable_ =  10.444 45.3708 42.5252 3.6632
has sdev of variable_ = 0.39605 15.032 11.1881 0.27605
 
sample_12 of experiment_2
has time =  11
has variable_ =  11.4506 25.0062 51.3984 4.2621
has sdev of variable_ = 1.2365 7.628 11.911 0.10338
 
sample_13 of experiment_2
has time =  12
has variable_ =  12.1132 10.8632 57.676 4.5932
has sdev of variable_ = 1.6628 5.9917 4.7474 0.43529
 
sample_14 of experiment_2
has time =  13
has variable_ =  12.659 2.0748 63.2968 4.9134
has sdev of variable_ = 1.7848 2.7651 3.6115 0.63442
 
sample_15 of experiment_2
has time =  14
has variable_ =  12.9694 0.0528 65.8565 5.072
has sdev of variable_ = 1.8987 0.07467 0.71064 0.91358
 
 
  
// INITIAL BOUNDS
variable_1 of experiment_1
has lowerInitialBound =  0.28683
has upperInitialBound =  0.35594
 
variable_2 of experiment_1
has lowerInitialBound =  98.3568
has upperInitialBound =  98.4905
 
variable_3 of experiment_1
has lowerInitialBound =  0
has upperInitialBound =  0.2
 
variable_4 of experiment_1
has lowerInitialBound =  0
has upperInitialBound =  0.2
 
variable_1 of experiment_2
has lowerInitialBound =  0.018304
has upperInitialBound =  0.5031
 
variable_2 of experiment_2
has lowerInitialBound =  147.7309
has upperInitialBound =  154.7511
 
variable_3 of experiment_2
has lowerInitialBound =  0
has upperInitialBound =  0.2
 
variable_4 of experiment_2
has lowerInitialBound =  0
has upperInitialBound =  0.2
 
 
 
// INITIAL SOLUTION
 
 alpha has defaultInitialValue = 1
 
 beta has defaultInitialValue = 1
 
 g has defaultInitialValue = 0
 
 h has defaultInitialValue = 0
 
 
 end problem ss_ethanolferm1