
JAK-STAT

seed_ := 65$

NUMBER OF EQUATIONS$

n_ := 12$

VARIABLES VECTOR$

b_ := {x1,
x2,
x3,
x4,
x5,
x6,
x7,
x8,
x9,
u1,
y1,
y2}$

UNKNOWN PARAMETER(S) VECTOR$

b1_ := {p1,
p2,
p3,
p4,
p5,
p6,
p7}$

RANKING AMONG THE VARIABLES$

bb_ := {x1,
x2,
x3,
df(x1,t),
df(x2,t),
df(x3,t),
df(x1,t,2),
df(x2,t,2),
df(x3,t,2),
df(x1,t,3),
df(x2,t,3),
df(x3,t,3),
df(x1,t,4),
df(x2,t,4),
df(x3,t,4),
df(x1,t,5),
df(x2,t,5),
df(x3,t,5),
df(x1,t,6),
df(x2,t,6),
df(x3,t,6),
df(x1,t,7),
df(x2,t,7),
df(x3,t,7),
df(x1,t,8),
df(x2,t,8),
df(x3,t,8),
df(x1,t,9),
df(x2,t,9),
df(x3,t,9),
x4,
x5,
x6,
x7,
x8,
x9,
u1,
y1,
y2,
df(x4,t),
df(x5,t),
df(x6,t),
df(x7,t),
df(x8,t),
df(x9,t),
df(u1,t),
df(y1,t),
df(y2,t)}$

NUMBER OF INPUT(S)$

nu_ := 1$

NUMBER OF OUTPUT(S)$

ny_ := 2$

NUMBER OF STATE(S) $

nx_ := 9$

MODEL EQUATION(S)$

c_ := {df(x1,t)=(p4*p7*x9 - p6*u1)/p6,
df(x2,t)= - 2*p2*x2**2 + u1,
df(x3,t)=p2*x2**2 - p3*x3,
df(x4,t)=(p3*p6*x3 - p4*p7*x4)/p7,
df(x5,t)=(2*x4 - x5)*p4,
df(x6,t)=(x5 - x6)*p4,
df(x7,t)=(x6 - x7)*p4,
df(x8,t)=(x7 - x8)*p4,
df(x9,t)=(x8 - x9)*p4,
u1=p1*x1,
y1=(x2 + 2*x3)/p5,
y2=(x2 + 2*x3 + x1)/p5}$

CHARACTERISTIC SET$

aa_(1) := df(x2,t) - x1*p1 + 2*x2**2*p2$

aa_(2) := df(x3,t) - x2**2*p2 + x3*p3$

aa_(3) := df(x1,t,7) + df(x1,t,6)*(p1 + 6*p4) + 3*df(x1,t,5)*p4*(2*p1 + 5*p4) + 5*df(x1,t,4)*p4**2*(3*p1 + 4*p4) + 5*df(
x1,t,3)*p4**3*(4*p1 + 3*p4) + 3*df(x1,t,2)*p4**4*(5*p1 + 2*p4) + df(x1,t)*p4**5*(6*p1 + p4) + x1*p1*p4**6 - 2*x3*p3*p4**
6$

aa_(4) := df(x1,t,6)*p6 + df(x1,t,5)*p6*(p1 + 5*p4) + 5*df(x1,t,4)*p4*p6*(p1 + 2*p4) + 10*df(x1,t,3)*p4**2*p6*(p1 + p4) 
+ 5*df(x1,t,2)*p4**3*p6*(2*p1 + p4) + df(x1,t)*p4**4*p6*(5*p1 + p4) + x1*p1*p4**5*p6 - 2*x4*p4**6*p7$

aa_(5) := df(x1,t,5)*p6 + df(x1,t,4)*p6*(p1 + 4*p4) + 2*df(x1,t,3)*p4*p6*(2*p1 + 3*p4) + 2*df(x1,t,2)*p4**2*p6*(3*p1 + 2
*p4) + df(x1,t)*p4**3*p6*(4*p1 + p4) + x1*p1*p4**4*p6 - x5*p4**5*p7$

aa_(6) := df(x1,t,4)*p6 + df(x1,t,3)*p6*(p1 + 3*p4) + 3*df(x1,t,2)*p4*p6*(p1 + p4) + df(x1,t)*p4**2*p6*(3*p1 + p4) + x1*
p1*p4**3*p6 - x6*p4**4*p7$

aa_(7) := df(x1,t,3)*p6 + df(x1,t,2)*p6*(p1 + 2*p4) + df(x1,t)*p4*p6*(2*p1 + p4) + x1*p1*p4**2*p6 - x7*p4**3*p7$

aa_(8) := df(x1,t,2)*p6 + df(x1,t)*p6*(p1 + p4) + x1*p1*p4*p6 - x8*p4**2*p7$

aa_(9) := df(x1,t)*p6 + x1*p1*p6 - x9*p4*p7$

aa_(10) := u1 - x1*p1$

aa_(11) :=  - x2 - 2*x3 + y1*p5$

aa_(12) :=  - x1 - x2 - 2*x3 + y2*p5$

MODEL ALGEBRAICALLY OBSERVABLE$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S) VECTOR$

b2_ := {p1=63,p2=41,p3=38,p4=35,p5=32,p6=23,p7=8}$

EXHAUSTIVE SUMMARY $

flist_ := { - p1 + 63,
p2 - 41,
 - p2 + 41,
p3 - 38,
p1*p4**6 - 115810734375,
 - p3*p4**6 + 69854093750,
3*p1*p4**2 + 4*p4**3 - 403025,
4*p1*p4**3 + 3*p4**4 - 15306375,
5*p1*p4**4 + 2*p4**5 - 577740625,
6*p1*p4**5 + p4**6 - 21691534375,
p1 + 6*p4 - 273,
2*p1*p4 + 5*p4**2 - 10535}$

MODEL PARAMETER SOLUTION(S)$

 G_:=GROESOLVE(FLIST_,B1_) $

g_ := {{p2=41,p3=38,p1=63,p4=35}}$

MODEL NON IDENTIFIABLE$
Elapsed time for JAK-STAT: 2.0171877 seconds
