
Goodwin

seed_ := 25$

NUMBER OF EQUATIONS$

n_ := 4$

VARIABLES VECTOR$

b_ := {x1,x2,x3,y1}$

UNKNOWN PARAMETER(S) VECTOR$

b1_ := {p1,
p2,
p4,
p5,
p6,
p7,
p8}$

RANKING AMONG THE VARIABLES$

bb_ := {x1,
df(x1,t),
df(x1,t,2),
df(x1,t,3),
x2,
x3,
y1,
df(x2,t),
df(x3,t),
df(y1,t)}$

NUMBER OF INPUT(S)$

nu_ := 0$

NUMBER OF OUTPUT(S)$

ny_ := 1$

NUMBER OF STATE(S) $

nx_ := 3$

MODEL EQUATION(S)$

c_ := {df(x1,t)=(p1 - p2*p4*x1 - x3**p3*p4*x1)/(x3**p3 + p2),
df(x2,t)=p5*x1 - p6*x2,
df(x3,t)=p7*x2 - p8*x3,
x1=y1}$

CHARACTERISTIC SET$

aa_(1) := df(x1,t)*(x3**p3 + p2) + x1*p4*(x3**p3 + p2) - p1$

aa_(2) := x1 - y1$

aa_(3) := df(x2,t) - x1*p5 + x2*p6$

aa_(4) := df(x3,t) - x2*p7 + x3*p8$

MODEL NOT ALGEBRAICALLY OBSERVABLE$

NORMALIZED  INPUT /OUTPUT RELATION(S) $

aan_(1) := ( - df(x1,t)*(x3**p3 + p2) - x1*p4*(x3**p3 + p2) + p1)/p1$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S) VECTOR$

b2_ := {p1=8,p2=16,p4=3,p5=20,p6=17,p7=13,p8=5}$

EXHAUSTIVE SUMMARY $

flist_ := {(17*p1 - 8*p2 - 8)/(8*p1),(51*p1 - 8*p2*p4 - 8*p4)/(8*p1)}$

MODEL PARAMETER SOLUTION(S)$

 G_:=GROESOLVE(FLIST_,B1_) $

g_ := {{p1=(8*p2 + 8)/17,p4=3}}$

MODEL NON IDENTIFIABLE$

IDENTIFIABILITY WITH THE KNOWN INITIAL CONDITION(S)$

bi_ := {x1,y1,y1}$

aai_(2) := x1 - y1$

ic1_ := {}$

BBBI_ INCLUDES THE BB_ ENTRIES CALCULATED AT T=0$

bbbi_ := {df(x1,t)=x1d10,x1=x10,y1=y1_0}$

UNKNOWN PARAMETER(S) VECTOR$

b1i_ := {p1,
p2,
p4,
p5,
p6,
p7,
p8,
y1_0}$

EXHAUSTIVE SUMMARY EVALUATED AT TIME T=0 $

bbi_ := {x1d10,x10}$

flisty_ := {3*x3**p3*x10 + x3**p3*x1d10 + 48*x10 + 16*x1d10 - 8,x10 - 10}$

 GY_:=GROESOLVE(FLISTY_,BBI_)$

gy_ := {{x1d10=(2*( - 15*x3**p3 - 236))/(x3**p3 + 16),x10=10}}$

RANDOMLY CHOSEN NUMERICAL PARAMETER(S ) VECTOR$

b2i_ := {p1=8,p2=16,p4=3,p5=20,p6=17,p7=13,p8=5,y1_0=10}$

EXHAUSTIVE SUMMARY$

flist1i_ := {(17*p1 - 8*p2 - 8)/(8*p1),
(51*p1 - 8*p2*p4 - 8*p4)/(8*p1),
 - y1_0 + 10}$

GI_=GROESOLVE(FLIST1I_,B1I_)  $

gi_ := {{y1_0=10,p1=(8*p2 + 8)/17,p4=3}}$

MODEL NON IDENTIFIABLE$
Elapsed time for Goodwin: 1.0062868 seconds
