
GoodwinPoly

seed_ := 25$

NUMBER OF EQUATIONS$

n_ := 7$

VARIABLES VECTOR$

b_ := {x1,
x2,
x3,
xi1,
y1,
y2,
y3}$

UNKNOWN PARAMETER(S) VECTOR$

b1_ := {p1,
p3,
p4,
p5,
p6,
p7,
p8}$

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),
xi1,
y1,
y2,
y3,
df(xi1,t),
df(y1,t),
df(y2,t),
df(y3,t)}$

NUMBER OF INPUT(S)$

nu_ := 0$

NUMBER OF OUTPUT(S)$

ny_ := 3$

NUMBER OF STATE(S) $

nx_ := 4$

MODEL EQUATION(S)$

c_ := {df(x1,t)=p1*xi1 - p4*x1,
df(x2,t)=p5*x1 - p6*x2,
df(x3,t)=p7*x2 - p8*x3,
df(xi1,t)=( - x3**p3*(p7*x2 - p8*x3)*p3*xi1**2)/x3,
y1=x1,
y2=x2,
y3=x3}$

CHARACTERISTIC SET$

aa_(1) := df(x2,t) - x1*p5 + x2*p6$

aa_(2) := df(x3,t) - x2*p7 + x3*p8$

aa_(3) :=  - df(x1,t,2)*x3*p1 - x3**p3*df(x1,t)**2*x2*p3*p7 + x3**p3*df(x1,t)**2*x3*p3*p8 - 2*x3**p3*df(x1,t)*x1*x2*p3*
p4*p7 + 2*x3**p3*df(x1,t)*x1*x3*p3*p4*p8 - df(x1,t)*x3*p1*p4 - x3**p3*x1**2*x2*p3*p4**2*p7 + x3**p3*x1**2*x3*p3*p4**2*p8
$

aa_(4) := df(x1,t) + x1*p4 - xi1*p1$

aa_(5) :=  - x1 + y1$

aa_(6) :=  - x2 + y2$

aa_(7) :=  - x3 + y3$

MODEL ALGEBRAICALLY OBSERVABLE$

NORMALIZED  INPUT /OUTPUT RELATION(S) $

aan_(1) := df(x2,t) - x1*p5 + x2*p6$

aan_(2) := df(x3,t) - x2*p7 + x3*p8$

aan_(3) := (df(x1,t,2)*x3*p1 + x3**p3*df(x1,t)**2*x2*p3*p7 - x3**p3*df(x1,t)**2*x3*p3*p8 + 2*x3**p3*df(x1,t)*x1*x2*p3*p4
*p7 - 2*x3**p3*df(x1,t)*x1*x3*p3*p4*p8 + df(x1,t)*x3*p1*p4 + x3**p3*x1**2*x2*p3*p4**2*p7 - x3**p3*x1**2*x3*p3*p4**2*p8)/
p1$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S) VECTOR$

b2_ := {p1=8,p3=16,p4=3,p5=20,p6=17,p7=13,p8=5}$

EXHAUSTIVE SUMMARY $

flist_ := { - p5 + 20,
p6 - 17,
 - p7 + 13,
p8 - 5,
p4 - 3,
(10*p1 - p3*p8)/p1,
(2*( - 78*p1 + p3*p4*p7))/p1,
(2*(30*p1 - p3*p4*p8))/p1,
( - 26*p1 + p3*p7)/p1,
( - 234*p1 + p3*p4**2*p7)/p1,
(90*p1 - p3*p4**2*p8)/p1}$

MODEL PARAMETER SOLUTION(S)$

 G_:=GROESOLVE(FLIST_,B1_) $

g_ := {{p5=20,p6=17,p7=13,p8=5,p1=p3/2,p4=3}}$

MODEL NON IDENTIFIABLE$

IDENTIFIABILITY WITH THE KNOWN INITIAL CONDITION(S)$

BBBI_ INCLUDES THE BB_ ENTRIES CALCULATED AT T=0$

bbbi_ := {df(x3,t,4)=x3d40,
df(x2,t,4)=x2d40,
df(x1,t,4)=x1d40,
df(x3,t,3)=x3d30,
df(x2,t,3)=x2d30,
df(x1,t,3)=x1d30,
df(x3,t,2)=x3d20,
df(x2,t,2)=x2d20,
df(x1,t,2)=x1d20,
df(x3,t)=x3d10,
df(x2,t)=x2d10,
df(x1,t)=x1d10,
x3=x30,
x2=x20,
x1=x10,
x1=3/10,
x2=9/10,
x3=13/10,
xi1=1/((13/10)**p3 + p2),
y1=y1_0,
y2=y2_0,
y3=y3_0}$

UNKNOWN PARAMETER(S) VECTOR$

b1i_ := {p1,
p3,
p4,
p5,
p6,
p7,
p8,
y1_0,
y2_0,
y3_0}$

EXHAUSTIVE SUMMARY EVALUATED AT TIME T=0 $

bbi_ := {x1d20,
x3d10,
x2d10,
x1d10,
x30,
x20,
x10}$

flisty_ := { - 20*x10 + 17*x20 + x2d10,
 - 13*x20 + 5*x30 + x3d10,
8*x30*( - 234*x10**2*x20*x30**15 + 90*x10**2*x30**16 - 156*x10*x1d10*x20*x30**15 + 60*x10*x1d10*x30**16 - 26*x1d10**2*
x20*x30**15 + 10*x1d10**2*x30**16 - 3*x1d10 - x1d20),
(30000000000000000*p2*x10 + 10000000000000000*p2*x1d10 + 1996249827549539523*x10 + 665416609183179841*x1d10 - 
80000000000000000)/(10000000000000000*p2 + 665416609183179841),
 - x10 + 10,
 - x20 + 24,
 - x30 + 22}$

 GY_:=GROESOLVE(FLISTY_,BBI_)$

gy_ := {{x1d20=(10*(900000000000000000000000000000000*p2**2 + 119534989652972371380000000000000000*p2 - 
35391710386064940152877036624628830031445181270660932471))/(100000000000000000000000000000000*p2**2 + 
13308332183663596820000000000000000*p2 + 442779263776840698304313192148785281),
x2d10=-208,
x3d10=202,
x20=24,
x1d10=(10*( - 30000000000000000*p2 - 1988249827549539523))/(10000000000000000*p2 + 665416609183179841),
x10=10,
x30=22}}$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S ) VECTOR$

b2i_ := {p1=8,
p3=16,
p4=3,
p5=20,
p6=17,
p7=13,
p8=5,
y1_0=10,
y2_0=24,
y3_0=22}$

EXHAUSTIVE SUMMARY$

flist1i_ := { - p5 + 20,
p6 - 17,
 - p7 + 13,
p8 - 5,
p4 - 3,
(10*p1 - p3*p8)/p1,
(2*( - 78*p1 + p3*p4*p7))/p1,
(2*(30*p1 - p3*p4*p8))/p1,
( - 26*p1 + p3*p7)/p1,
( - 234*p1 + p3*p4**2*p7)/p1,
(90*p1 - p3*p4**2*p8)/p1,
2*( - 12*p7 + 11*p8 + 101),
(20*( - 12000000000000000000000000000000000*22**p3*p2**2*p3*p4**2*p7 + 11000000000000000000000000000000000*22**p3*p2**2*
p3*p4**2*p8 + 72000000000000000000000000000000000*22**p3*p2**2*p3*p4*p7 - 66000000000000000000000000000000000*22**p3*p2
**2*p3*p4*p8 - 108000000000000000000000000000000000*22**p3*p2**2*p3*p7 + 99000000000000000000000000000000000*22**p3*p2**
2*p3*p8 - 1596999862039631618400000000000000000*22**p3*p2*p3*p4**2*p7 + 1463916540202995650200000000000000000*22**p3*p2*
p3*p4**2*p8 + 9562799172237789710400000000000000000*22**p3*p2*p3*p4*p7 - 8765899241217973901200000000000000000*22**p3*p2
*p3*p4*p8 - 14315398758356684565600000000000000000*22**p3*p2*p3*p7 + 13122448861826960851800000000000000000*22**p3*p2*p3
*p8 - 53133511653220883796517583057854233720*22**p3*p3*p4**2*p7 + 48705719015452476813474451136366380910*22**p3*p3*p4**2
*p8 + 317523470029693597484385498347125402320*22**p3*p3*p4*p7 - 291063180860552464360686706818198285460*22**p3*p3*p4*p8 
- 474376485210092838284498247520688103480*22**p3*p3*p7 + 434845111442585101760790060227297428190*22**p3*p3*p8 + 
3300000000000000000000000000000000*p1*p2**2*p4 - 9900000000000000000000000000000000*p1*p2**2 + 
438294962060898695060000000000000000*p1*p2*p4 - 1314884886182696085180000000000000000*p1*p2 + 
14553159043027623218034335340909914273*p1*p4 + 389308814246714341681647402870917130345896993977270257181*p1))/(
100000000000000000000000000000000*p2**2 + 13308332183663596820000000000000000*p2 + 442779263776840698304313192148785281)
,
(100000000000000000*(13/10)**p3*p2*p4 - 300000000000000000*(13/10)**p3*p2 + 6654166091831798410*(13/10)**p3*p4 - 
19882498275495395230*(13/10)**p3 - 10000000000000000*p1*p2 - 665416609183179841*p1 + 100000000000000000*p2**2*p4 - 
300000000000000000*p2**2 + 6654166091831798410*p2*p4 - 19882498275495395230*p2)/(10000000000000000*(13/10)**p3*p2 + 
665416609183179841*(13/10)**p3 + 10000000000000000*p2**2 + 665416609183179841*p2),
y1_0 - 10,
y2_0 - 24,
y3_0 - 22}$

GI_=GROESOLVE(FLIST1I_,B1I_)  $

gi_ := {}$

MODEL NON IDENTIFIABLE$
Elapsed time for GoodwinPoly: 1.0133736 seconds
