Systems Innovation 1 General System Theory
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1 Systems Iovto Geerl System Theory Prof. Furut, K. UTYO Wht s system? Fetures of system Ihomogeeous ofte herrchcl Iterctos betwee compoets Globl orer Gol-orete cse of hum-me system Emples of system Solr system, orgsms, br Power plt, utomoble fctory, Iteret Ecology of Tokyo by, globl evromet Ecoomy of Jp, mecl surce, uversty
2 System s the wy how you look t object Wht o you see? Youg ly Ol wom Wht orgzto s the Uv. of Tokyo? It proves/prouces Hgher eucto Flesh hum resources Slry Foos etertmet Lots of wste Geerl system theory Allometrc prcple Relto observe vrous res of bology y b y y Costt growth rto betwee y Fmlr lso ecoomy : elstcty
3 Geerl system theory Bertlffy s growth equto Fts growth curves of lmost speces w w w legth cm Growth of sturgeo 5 5 mesure theory 3 yers Stte equtos Geerl escrpto of ymc system f,,, f,,, f,,,,,, : Stte vrbles 3
4 Stte spce trjectory Stte spce Phse spce compose of stte vrbles Ech stte s represete s pot the stte spce 3 q Trjectory qt Shows ymc behvour of the system Emple ketcs m k k m Stte vrbles, k m m = 3 k =.5 m = m = k = 4
5 5 Emple electrocs u R R L C v v R u L R v v C u R R L C R R CL R u R CL L C R R R R R CL, Emple bochemstry 3 X schrge K K 3 k 3 k k K k k k k k k X K
6 Emple worl poltcs Rchrso moel Arms rce betwee two oppoets Armmet proporto to oppoet s cto Dsrmmet ue to the lo to tol ecoomy Ltet cetve towr rmmet ky g y l y h Frst orer ler system t e t / t 6
7 7 Seco orer ler system Stte equtos Egevlues c b bc c b A I 4 bc D Two rel egevlues D> l l l l, e w e w t t t
8 Two rel egevlues D> t t t w e w e, l l l l Two rel egevlues D> t t t w e w e, l l 8
9 Sgle rel egevlue D= t t w w t e, l l Cojugte comple egevlues D< j t t e w s t w cos t, 9
10 Cojugte comple egevlues D< t w s t w cos t, Behvour rou equlbrum pot Stble pot Ustble pot Sle pot Crculto ceter
11 Ketc equto System escrpto wth th-orer ODE Stte vrbles c be efe s follows 3 Ketc equto Rewrte ketc equto Equvlet stte equtos 3
12 Emple of populto ymcs Lotk-Volterr moel Two speces wth competto Lmtto of resources Prey-pretor relto N N : trspecfc N N N N N N : terspecfc competto coeff. Behvor of L-V moel N N : N or : N or N N N N Four fe equlbrum pots P :, P :, P :, P 3 : N *, N *
13 Behvor of L-V moel N N / / / / / / N / / N N N / / / / N / / / / N Prey-pretor system No trspecfc competto N N N N N N Prey N pretor N Pretor huts ets prey. Pretor cot survve wthout prey. Pretor brees rply, f prey s ffluet. 3
14 Behvor of pretor-prey system 4 N N N t / P.,.,.,. / N Wth trspecfc competto N N N N N N N N Three fe pots P :, P :, P : N *, N * 4
15 Behvor wth trspecfc competto N N / / N / / / N / Geerl moel of ymc system Isomorphsm fferet fels of scece Oe-to-oe correspoece betwee the elemets of fferet systems Movemet ketc system physcs Chemcl recto chemstry Growth of orgsms bology Populto ecosystem ecology Growth of cptl ecoomy ecoomy Estece of geerl moel tht epls behvour of ymc systems clug ophyscl pheome 5
16 Geerl lw of physcs Tetrhero of sttes q fq,e,c = e e = Et f = q/ fe,f,r = Ohm s lw e = p/ f = Ft f f3p,f,l = p qutty effort e flow f mometum p splcemet q ketc force N velocty m/s mometum N s splcemet m electrcl voltge V curret A mg.flu V s chrge C hyrulc pressure P flow m 3 /s volume m 3 therml temp.ff. K het flu W het J Etee geerl lw of physcs Geerl lw of flow q fq,e,c = e e = Et f = q/ fe,f,r = Ohm s lw e = p/ f = Ft f f3p,f,l = p qutty effort e flow f splcemet q ffuso esty gret mss flu esty tre buce of goos goos flow stock fce vestmet potetl moey stock culture cretvty formto soft power 6
17 Itercto recto rte Itercto System compoets mke mpcts o ech other Collso, grvty, chemcl tercto, commucto, seul reproucto, trg, tertol coflct,... Drect/remote, b-rectol/urectol Recto Iterctos result some chges system sttes Recto rte Tmes or esty of rectos tht occur per ut tme Icreses whe the umber of relevt ettes crese Frst-orer recto A system compoet chges ts sttus spoteously, usully ecys to other etty. Recto rte costt k Probblty tht the compoet ecys per ut tme X k t kx X X e Hlf-lfe T / Tme requre for qutty to fll to hlf T / l k 7
18 Emple of frst-orer recto Decy of roctve ucleus 6 Co 6 N + e =5.7yr l Flure of compoets Relblty t tme t wth costt flure rte 9 s P e t Seco-orer recto Compoet X Y rectly tercts to yel ew compoets The recto rte s proportol to the prouct of the umber esty of X tht of Y X Y kxy X Seco-orer recto by two Xs X kx X X X kt k X X X t k X X kt X X 8
19 Emple of seco-orer recto Hutg Lotk-Volterr moel Purchse of goos trggere by wor of mouth Chemcl recto X + Y Z Seul reproucto Proportol to the chce of prg B mxy m N Hgher-orer recto X + Y + Z + Progress of rectos X X Y Recto rte p v kx Y q Y Z r Totl orer of recto p q r Z Z 9
20 Zero-orer recto Recto rte oes ot epe o the umber or esty of relevt ettes. X k X X k t Itl esty furut/techg/s/
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