T?

1
T?µa ?e??t? t?? d??aµ???? s?µpe??f???? aµ?????
?a? ap??? s??a????sµ?? d?? µ????ß?a??? p????sµ??
se d??ta?? d?? s??e??µ???? ??µ?stat??.
?a???s?as? ??at??ß?? ???

• G??? ??e???d?a
• ??µ???? ???a????? ?.?.
• ?pe?????? ?a????t?? S.?a????

S?????????S 2006
2
????????

• ???s? µ??t?? ?a???e??e??? µ???????a??sµ?? se
  p????? ß??µ??a????? d?e??as?e?.
• ? s??a????sµ?? (Fredrickson Stephanopoulos,
  1981) e??a? ? p?? ????? µ????ß?a?? a????ep?d?as?
  
• ?µ???? ?a? ap??? s??a????sµ??
• ???s?µ???s? e??ast???a?? se ??a ??µ?st?t?.
• ?as??? e??t?µa µp????? ?? s??a??????µe???
  p????sµ?? ?a s???p?????? ?a? ?p? p??e? s?????e?

3
??µ?st?t??

• ???µ?? a?a??s??, D
• ??d???? ???µ?? a??pt????, µ
• ?e?????st??? s?stat???

4
???t??a a??pt????

• ???t??? Monod (1942)

• µm µ???st?? e?d???? ???µ?? a??pt????
• K sta?e?? ???esµ?? ? sta?e?? Michaelis
• ???t??? Andrews

• K ? sta?e?? pa?eµp?d?s??
• µmaxµ/(12v(?/?))

5
??as??p?s? ?e???t???? µe?et?? ??a t?? ap?? ?a?
aµ??? s??a????sµ?
S?????e? ?e?et?t?? S?µp??asµa
??a? ??µ?st?t??, ste??a t??f?d?s?a, sta?e??? ?e?t???????? s?????e?. Powell (1958) µ??t??? Monod Aris Humphrey (1977) µ??t??? Andrews S???pa??? µ??? ??a d?a???t?? t?µ?? t?? ???µ?? a?a??s??, ?ta? ?? ?aµp??e? t?? e?d???? ???µ?? a??pt???? t?µ???ta?.
??? s??e??µ???? ??µ?st?te?, ßa?µ?st?t??, ste??a t??f?d?s?a, sta?e??? ?e?t???????? pa??µet???. Stephanopoulos Fredrickson (1979) Kung Baltzis (1987) Jager et al. (1987) Smith Tang (1989) µ??t??? Monod Lenas et al (1998) µ??t??? Andrews S???pa??? se µ???µ? ?a? ?p? s?????e?, se pe???d??? ?at?stas? ??a µ?a s?et??? e??e?a pe????? t?? pa?aµ?t??? ?e?t?????a?, ?ta? ?? ?aµp??e? t?? e?d???? ???µ?? a??pt???? t?µ???ta?.
6
S?????e? ?e?et?t?? S?µp??asµa
??a? ??µ?st?t??, µ? ste??a t??f?d?s?a, sta?e??? ?e?t???????? pa??µet???. A.Ajbar K.Alhumazi, ??p??µat??? e??as?a ?.Te?d???? (2005) - ???t??? Andrews S???pa??? se µ???µ? ?a? ?p? s?????e?, se pe???d??? ?at?stas?, ??a µ?a s?et??? e??e?a pe????? t?? pa?aµ?t??? ?e?t?????a?, ?ta? ?? ?aµp??e? t?? e?d???? ???µ?? a??pt???? t?µ???ta?.
7
??t??e?µe?? ??at??ß??

• ?e??t? t?? d??aµ???? s?µpe??f???? aµ??o?? ?a?
  ap??? s??a????sµ?? d?? µ????ß?a??? p????sµ?? se
  d?? s??e??µ????? ??µ?st?te?, ?a??? µetaß???eta?
  t? s?et??? µ??e??? t??? ?a? ? ßa?µ?? s??e????
  t???.
• ???tas? t?? ep?d?as?? st? d??aµ??? t?? s?st?µat??
  t?? ?pa???? µ???????a??sµ?? st? ?e?µa t??f?d?s?a?
  t?? d?? ??µ?stat??.

8
?e????af? s?st?µat??
2 s??e??µ???? CSTR
F2f , S2f , C12f , C22f
F1f , S1f , C11f ,C21f
F2e
F1e
V1
V2
F1c
F2c
9
?s?????a µ??a?

• ?s?????a µ??a? ??a t?? 1? ??µ?st?t?

• e?s???

• e????

• pa?a????

10

• ?s?????a µ??a? ??a t?? 2? ??µ?st?t?

• ?s?????a pa?????
• F2f F1c F2e F2c
• F1f F2c F1e F1c

11
?a?ad????

• ?µe??t??? ? e?d??e??? µetaß???sµ??.
• ?ata????s? ?p?st??µat?? µ??? ??a t? s???es?
  ß??µ??a?.
• ??? p??s?????s? ??tt???? sta t????µata t??
  ??µ?st?t?.
• ?a?eµp?d?st??? d??s? t?? ?p?st??µat?? se µe???e?
  s???e?t??se?? ???s? µ??t???? Andrews.
• ?e??pt?s? ßa?µ?st?t? (Lovitt Wimpenny, 1981)
• ???µ?? ???? st?? e?s?d????µ?? ???? st?? ???d?
• F1eF1f, F2eF2f
• ?s?? ???µ?? ep????????a? µeta?? t?? d??
  a?t?d?ast????
• F1cF2c

12
?d?astat?p???s?
?etaß??t??
?a??µet???


??d???? ???µ?? a??pt???? p????sµ?? ?- p???
?- p???
?a?ad??? ßa?µ?st?t? vu1
13
???s?se??
14
????d??
???tas? d??aµ???? s?st?µat?? µe ???s? µe??d?? t?? ?e???a? d?a??ad?se??
?e????af? s?st?µat?? µ?s? e??? s?st?µat?? S.?.?

???es? µ???µ?? ?atast?se?? s?st?µat?? xs
f(xsp)0
G?aµµ???p???s? ???? ap? µ?a ?.? ?a? ?p?????sµ?? ?d??t?µ?? Ia??ß?a??? p??a?a

???es? d?a??ad?se?? µ???µ?? ?atast?se??.
15
?p?????sµ?? pe???d???? ??se??.
?p?????sµ?? ?a?a?t???st???? p???ap?as?ast?? (p??/st?? Floquet) t?? pe???d???? ??se?? (???a??? ??????).

???es? d?a??ad?se?? ???a??? ??????
?atas?e?? ?e?t???????? d?a???µµat??
?e??t? e?st??e?a? pe???d???? ??se??.
16
??p???? ??a??ad?se?? s?st?µ?t?? µe µetaß??? µ?a?
pa?aµ?t???
17
(No Transcript)
18
?????? d?a??ad?se??

• ?e? ?p???e? µetaß??? t?? e?st??e?a? s?µe???
  ?s????p?a? ? ???a??? ??????
• ?p???e? µ?a ????? µetaß??? t?? e????a? t?? ?????
  t?? f?se??.
• ?te???????? s??des? a????ep?d?as? t?? e?sta????
  ?a? t?? asta???? p???ap??t?ta? d?? sa?µat????
  s?µe???.
• ?µ??????? s??des? a????ep?d?as? t?? e?sta????
  ?a? t?? asta???? p???ap??t?ta? t?? ?d???
  sa?µat???? s?µe???.
• ?µf???s? ???a??? ??????
• ?µf???s? fa???µ???? p???e?st??e?a?

19
????sµ???

• XPPAUT
• ??a e??a?e?? ??a t?? p??s?µ???s? ?a? a????s?
  d??aµ???? s?st?µ?t?? (Bard Ermentrout).
• ?p???s? d?af?????? e??s?se??, e??s?se?? d?af????,
  ?st???s??, s??a?t?s?a???, e??s?se?? ???a??? t?µ??
  ?a? st??ast???? e??s?se??.
• ??s? t?? AUTO
• ??t?p??e? ???d??? µ???µ?? ?atast?se?? ?a? ta
  s?µe?a d?a???d?s??
• ???e? d??-pa?aµ?t??? s?????s? d?a??ad?se??
• M.?-t?p?? ???a??? s?µe??? ?a? s?µe??? ?opf
• ???a??? ??????-t?p?? ???a??? s?µe???-LP,
  d?p?as?asµ?? pe???d??-PD ?a? Neimark-TR.
• ?e? µp??e? ?a ???e? d??-pa?aµ?t??? s?????s?
  µeta???s?µ?? d?a??ad?se?? µ???µ?? ? pe???d????
  ?atast?se??.
• ?e? e?t?p??e? ?????? d?a??ad?se??.

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????sµ???

• MATLAB/MATCONT (2002)
• ?a??t? s?????s?? t?? Matlab µe µ?a GUI ??a t??
  a???µ?t??? µe??t? pa?aµet????? µ? ??aµµ???? S??.
• ?p?t??pe? t?? ?p?????sµ? ?aµp????
• ?s????p?a?, ???a??? s?µe???, s?µe??? Hopf,
  ???a??? ??????, d?a??ad?se?? t?p?? ???a???
  s?µe???, d?p?as?asµ?? pe???d??, t????, s?µe???
  d?a??ad?se?? ???a??? ?????? ?a? s?µe???
  ?s????p?a?.
• ???a? d??at?? ? p??sd????sµ?? d?a??ad?se??
  s??d??stas??-2 (cusp, Bogdanov-Takens,
  generalized Hopf, zero-Hopf, double Hopf) se
  ?aµp??e? s?????s?? ???a??? s?µe??? ?a? ?aµp??e?
  Hopf.

21
?????aµµa d?a??ad?se?? M.K ??a ste??a t??f?d?s?a
Norm
L
22
?????aµµa d?a??ad?se?? pe???d???? ??se?? ??a µ?
ste??a t??f?d?s?a
?1
L
23
?a??µet??? s?st?µat??
?at?????a ?d??state? pa??µet??? ??????
???t??? a??pt???? a, ß, ?1, ?2 4
?e?t?????a µ? ste??a t??f?d?s?a u1, u2, x1f, x2f, y1f, y2f, z1f, z2f, r 9
?e?t?????a ste??a t??f?d?s?a u1, u2, z1f, z2f, r 5
??t?d?ast??e? ? 1
?? ste??a t??f?d?s?a 14
Ste??a t??f?d?s?a 10
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?p????? sta?e??? pa?aµ?t???

• ????p??es? s???pa???? se e?sta?? pe???d???
  ?at?stas? se ??a ??µ?st?t?.
• ?? ?aµp??e? t?? e?d???? ???µ?? a??pt???? (µ??t???
  Andrews) p??pe? ?a t?µ???ta? µe a?t??et? ???s?
  (d?p?. ?.Te?d???? 2005)
• a0.9, ß0.25, ?10.5, ?21.0
• ?p????? t?µ?? pa?aµ?t??? ?e?t?????a? ap? t?
  ?e?t??????? d????aµµa U vs yf ??a ??a ??µ?st?t?
  (d?p?. ?.Te?d???? 2005)
• x1f0.01, y1f0.1, z1f6, u10.4095
• ?d?e? s?????e? t??f?d?s?a? ?a? st??? d??
  ??µ?st?te?
• x1fx2f, y1fy2f, z1fz2f, u1u2

25
?aµp??e? e?d???? ???µ?? a??pt????

• ?a??µet??? µ??t???? Andrews a0.9, ß0.25,
  ?10.5, ?21.0

26
?e?t??????? ?????aµµa U vs Yf ??a 1 ??µ?st?t?
HP
LP
LP
?e????? ????µ?? ?a? ?a?/?a? ?.?, ij3 ????µ?? ?a? ?a?/?a? ?.?, ij3 ????µ?? ?a? ?a?/?a? ?.?, ij3
? S - -
?? S,S SP -
??? S,S,S SP,SP -
?V S,S SP,SP UN ? UF

• Se?sta??? ??µß?? ? est?a, SPsa?µat??? s?µe??,
  UNasta??? ??µß??, UFasta??? est?a.

27
(No Transcript)
28
?p?te??sµata

• 2 ?e?t??????? d?a???µµata ?.? ?? p??? t??
  pa?aµ?t???? L,R
• ?a???s?a µ???????a??sµ?? st?? t??f?d?s?a
• ?p? ste??a t??f?d?s?a
• ???a?e? e?st??e?a? ?.?
• ???es? d?a??ad?se?? pe???d???? ??se??

29
?? ste??a t??f?d?s?a

• ???at?t?ta eµf???s?? µ??? s???pa???? se µ???µ?
  ?a? e?de??µ???? se pe???d???, ????e? pe???d??? ?
  ?a? ?a?t??? ?at?stas?.
• ??????a? s??????? 21 d?a??ad?se?? ?.?, e? t??
  ?p???? 15 d?a??ad?se?? ???a??? s?µe??? ?a? 6
  d?a??ad?se?? Hopf.
• ?atas?e??st??e p??a?a? e?st??e?a? ?.? ??a ???eµ?a
  ap? t?? 138 pe?????? t?? ?e?t????????
  d?a???µµat??.
• ??a?????st??a? s??????? 84 d?af??et??? s??µata
  e?st??e?a?, µe 1 ??? ?a? 7 e?sta?e?? ?.?
  s???pa????.

30

• Sta?e??? ?e?t???????? pa??µet??? u1u20.4095,
  x1fx2f0.01, y1fy2f0.1, z1fz2f6

31

• ?? d?a??ad?se?? Hopf ?.? (hp4, hp3) s??d???ta? µe
  t?? ?pa??? e?sta???? ???a??? ??????.
• ? d?a???d?s? hp4 s?µat?d?te? t?? ?atast??f? e???
  ???a??? ?????? p?? d?µ?????e?ta? µ?s? µ?a? ??????
  d?a???d?s?? ?µ???????? s??des??.
• ? d?a???d?s? hp3 e??a? ap?t??esµa t?? s??e????
  t?? d?? ??µ?stat??, ?a??? ?f?stata? ??a
  Rgt0.00034, e?? ??e? ?? ???e? d?a??ad?se?? ?opf
  ?e?????? ap? R0.

32
??µ??????a ???a??? ?????? µ?s? ?µ????????
s??des?? ?a? ?atast??f? µ?s? t?? hp4

• L0.99442

• L0.99524

• L0.995913

• L0.99803

• ??a???d?s? Hopf hp4 L0.99608, R0.002

33
S?????s? d?a???d?s?? Hopf ?.?-hp3
34
S?????s? ?? p??? L t?? pe???d???? ??se?? ap? t??
hp3

• R0.0008

35
S?????s? d?a??ad?se?? pe???d???? ??se?? - hp3.
36
??µ??????a e?sta???? t????

• R0.0008, L1.0005

• ??µ? z11.2.

37
??a???d?s? d?p?as?asµ?? pe???d??
38
???a??? ?????? µeta?? d?ad?????? d?p?as?asµ??
pe???d??
39
Ste??a t??f?d?s?a

• ???a??? t?p?? µ???µ?? ?atast?se??
• ????? ??p??s? x1x2y1y20
• ??p??s? t?? p????sµ?? ?, x1x20, y1gt0,y2gt0
• ??p??s? t?? p????sµ?? ?, y1y20, x1gt0,x2gt0
• S???pa??? t?? d?? p????sµ??, x1gt0,x2gt0,y1gt0,y2gt0
• ???sd????st??a? s??????? 23 d?a??ad?se?? ?.?, e?
  t?? ?p???? 6 µeta???s?µe?, 13 ???a??? s?µe??? ?a?
  4 d?a??ad?se?? Hopf ?.?.
• ?atas?e??st??a? 3 p??a?e? e?st??e?a? ?.?.

40

• z1fz2f6, u1u20.4095

41

• Fa???µe?? p???e?st??e?a?
• Se µ?a pe????? ???? ap? t? L1 (?d??? ??µ?st?te?)
  ?a? ??a µ?????? ßa?µ??? s??e???? (Rlt0.005)
  ?p?????? ??? 9 e?sta?e?? ?.?
• ????? ?p??s?
• 2 ?atast?se?? ep????t?s?? t?? p????sµ?? ?
• 3 ?atast?se?? ep????t?s?? t?? p????sµ?? ?
• 2 ?atast?se?? s???pa???? t?? d?? p????sµ??
• ?p? t?? 4 d?a??ad?se?? ?opf, t?e?? (hp1, hp2,
  hp4) ?d????? st? d?µ??????a e?sta??? ???a???
  ??????.
• ?atast??f? ???a??? ?????? µ?s? ?????? d?a???d?s??
  ?µ???????? s??des??.

42
??µ??????a ?a? ?atast??f? ???a??? ?????? ???? ap?
t?? hp1

• L0.9776

• L0.9777

• L0.9775

• L0.97748

• Hp1 L0.97763, R0.002

43
S?µpe??sµata

• ? s??e??? d?? ??µ?stat?? d?µ?????e? t??
  apa?a?t?te? s?????e? ??????? a??µ??????e?a? ??a
  s???pa??? 2 p????sµ?? ?p? s??a????sµ?, ?ta? ??
  ?aµp??e? t?? e?d???? ???µ?? a??pt???? t???
  t?µ???ta?.
• ????p??es? ??a s???pa??? se pe???d??? ?at?stas?
  e??a? a?t??ete? ???se?? st? s?µe?? t?µ??.
• ? ?pa??? µ???????a??sµ?? st?? t??f?d?s?a p???a?e?
  fa???µe?a ????e? pe???d???t?ta? ?a? d?p?as?asµ??
  pe???d??.
• ?p? ste??a ?a? µ? t??f?d?s?a e??a? ??t??? ?
  p???e?st??e?a ?a? ta pe???d??? fa???µe?a, ?ts?
  ??p???? ??e???? ?a p??pe? ?a efa?µ??eta? st?
  ßa?µ? s??e???? R ??a ded?µ??? µ??e???
  a?t?d?ast????, ??a ep?te??? e?sta???? s???pa????
  se µ???µ? ? pe???d??? ?at?stas?.