: . .. : . 2006

. (Fredrickson & Stephanopoulos, 1981) . : ;

, D ,

Monod (1942)m: K : Michaelis AndrewsK: max=*/(1+2(/))

o , .

.

2 CSTRF2cF2eF2f , S2f , C12f , C22fF1f , S1f , C11f ,C21fF1eV1V2F1c

1

:F2f + F1c = F2e + F2cF1f + F2c = F1e + F1c 2

. . . Andrews. (Lovitt & Wimpenny, 1981): = :F1e=F1f, F2e=F2f : F1c=F2c

. : . : .

XPPAUT (Bard Ermentrout). , , , , . AUTO: - M.-: opf -: -LP, -PD Neimark-TR. - . .

MATLAB/MATCONT (2002) Matlab GUI . : , , Hopf, , , , , . -2 (cusp, Bogdanov-Takens, generalized Hopf, zero-Hopf, double Hopf) Hopf.

M.K LNorm

1L

. ( Andrews) (. . 2005): =0.9, =0.25, 1=0.5, 2=1.0 U vs yf (. . 2005): x1f=0.01, y1f=0.1, z1f=6, u1=0.4095 :x1f=x2f, y1f=y2f, z1f=z2f, u1=u2

Andrews: =0.9, =0.25, 1=0.5, 2=1.0

U vs Yf 1 S: , SP: , UN: , UF: .LPLPHP

2 . {L,R}: .

, . 21 ., 15 6 Hopf. . 138 . 84 , 1 7 . .

: u1=u2=0.4095, x1f=x2f=0.01, y1f=y2f=0.1, z1f=z2f=6

Hopf . (hp4, hp3) . hp4 . hp3 , R>0.00034, opf R=0.

hp4L=0.99442L=0.99524L=0.995913L=0.99803 Hopf hp4: L=0.99608, R=0.002

Hopf .-hp3

L hp3R=0.0008

- hp3.

R=0.0008, L=1.0005 z1=1.2.

: x1=x2=y1=y2=0 , x1=x2=0, y1>0,y2>0 , y1=y2=0, x1>0,x2>0 , x1>0,x2>0,y1>0,y2>0 23 ., 6 , 13 4 Hopf .. 3 ..

z1f=z2f=6, u1=u2=0.4095

L=1 ( ) (R

hp1L=0.9777L=0.9776L=0.9775L=0.97748Hp1: L=0.97763, R=0.002

2 , . . . , R , .