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phoenix708

Ìú¸Ëľ³æ (ÖøÃûдÊÖ)

[ÇóÖú] »áÓÃmatlabµÄͬ־°ï°ïæ¹þ£¡

dX/dt=1.98S(1-X)-0.73XY
dY/dt=dX/dt-0.00207Y/(1+Y+2S)-0.059d[Y/(1+Y+2S)]/dt
2dS/dt=-dX/dt-0.00056S/(1+Y+2S)-0.086d[S/(1+Y+2S)]/dt
µ±t=0ʱ,X=0,Y=0,S=1,
ÆäÖÐ tµÄ×î´óֵΪ3£¬
ÇóX£¬Y, SÓëtµÄ¹ØÏµÍ¼
лл!
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» ²ÂÄãϲ»¶

» ±¾Ö÷ÌâÏà¹Ø¼ÛÖµÌùÍÆ¼ö£¬¶ÔÄúͬÑùÓаïÖú:

ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

scumat

½ð³æ (ÕýʽдÊÖ)


ÎÊÌâºÜÄÑ£¬20¸ö½ð±ÒÉÙÁË¡£
2Â¥2012-01-05 16:40:17
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

phoenix708

Ìú¸Ëľ³æ (ÖøÃûдÊÖ)

ÒýÓûØÌû:
Â¥: Originally posted by scumat at 2012-01-05 16:40:17:
ÎÊÌâºÜÄÑ£¬20¸ö½ð±ÒÉÙÁË¡£

ÄãÄܽâÂð£¿Äܽâ¾Í¿ÉÒÔ¼Ó½ð±Ò
3Â¥2012-01-05 16:46:35
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

phoenix708

Ìú¸Ëľ³æ (ÖøÃûдÊÖ)

ÎÒ°Ñ·½³Ì×黯¼òÁËһϣ¬²»Öª¶Ô·ñ£¿¶®µÃ³æÓѰïæÔËËãÏ£¬Ó¦¸Ã²»ÄÑ£¡x'=1.98S*(1-X)-0.73*X*Y;                       
y'=x'-0.00207Y/(1+Y+2*S)-0.059*(y'/(1+y+2*s)+y*(y'+2*s')/(1+y+2*s)^2);         
s'=0.5*(-x'-0.00056S/(1+Y+2*S)-0.086*(s'/(1+y+2*s)+s*(y'+2*s')/(1+y+2*s)^2))
ÆäÖÐy'=dy/dt, s'=ds/dt£¬x'=dx/dt
4Â¥2012-01-05 17:49:11
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

dbb627

ÈÙÓþ°æÖ÷ (ÖøÃûдÊÖ)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

¸Ðл²ÎÓ룬ӦÖúÖ¸Êý +1
>> syms t
>> Y=sym('Y(t)')

Y =

Y(t)

>> S=sym('S(t)')

S =

S(t)

>> F=Y/(1+Y+2*S)

F =

Y(t)/(2*S(t) + Y(t) + 1)

>> dF=diff(F,t)

dF =

diff(Y(t), t)/(2*S(t) + Y(t) + 1) - (Y(t)*(2*diff(S(t), t) + diff(Y(t), t)))/(2*S(t) + Y(t) + 1)^2

1£ºÏȽ«¹«Ê½ÖеÄÏî¡°d[Y/(1+Y+2S)]/dt¡±Çóµ¼Õ¹¿ª±äΪ£º
    y'/(1+y+2*s)+y*(y'+2*s')/(1+y+2*s)^2£¬ÆäÖÐy'=dy/dt, s'=ds/dt
2£ºÍ¬Àí½«¡°d[S/(1+Y+2S)]/dt¡±±äΪ£º
   s'/(1+y+2*s)+s*(y'+2*s')/(1+y+2*s)^2
ÓÃmatlab ode15i½âÒþʽ΢·Ö·½³Ì
CODE:
odefun=@(t,x,dx)[dx(1)-1.98*x(3)*(1-x(1))+0.73*x(1)*x(2)
    dx(2)-(dx(1)-0.00207*x(2)/(1+x(2)+2*x(3))-0.059*(dx(2)/(1+x(2)+2*x(3))+x(2)*(dx(2)+2*dx(3))/(1+x(2)+2*x(3))^2))
    2*dx(3)+dx(1)+0.00056*x(3)/(1+x(2)+2*x(3))+0.086*(dx(3)/(1+x(2)+2*x(3))+x(3)*(dx(2)+2*dx(3))/(1+x(2)+2*x(3))^2)];
t0=0;
x0=[0 0 1]';
fix_x0=ones(3,1);
dx0=[0 1 1]';
fix_dx0=zeros(3,1);
[x02,dx02]=decic(odefun,t0,x0,fix_x0,dx0,fix_dx0);
solution=ode15i(odefun,[0 3],x02,dx02);
t=solution.x;
x=solution.y;
plot(t,x)
legend('X','Y','S')

[ Last edited by dbb627 on 2012-1-5 at 18:29 ]
The more you learn, the more you know, the more you know, and the more you forget. The more you forget, the less you know. So why bother to learn.
5Â¥2012-01-05 18:23:40
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

dbb627

ÈÙÓþ°æÖ÷ (ÖøÃûдÊÖ)

¡¾´ð°¸¡¿Ó¦Öú»ØÌû


phoenix708(½ð±Ò+30): ¡ï¡ï¡ïºÜÓаïÖú 2012-01-05 20:02:35
×öͼÈçÏÂ




[ Last edited by dbb627 on 2012-1-5 at 18:30 ]

» ±¾ÌûÒÑ»ñµÃµÄºì»¨£¨×îÐÂ10¶ä£©

The more you learn, the more you know, the more you know, and the more you forget. The more you forget, the less you know. So why bother to learn.
6Â¥2012-01-05 18:25:08
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

Ö¥Ö¥»¨

Í­³æ (³õÈëÎÄ̳)

ÒýÓûØÌû:
6Â¥: Originally posted by dbb627 at 2012-01-05 18:25:08:
×öͼÈçÏÂ

[ Last edited by dbb627 on 2012-1-5 at 18:30 ]

Thank you!
7Â¥2012-01-05 19:23:56
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

scumat

½ð³æ (ÕýʽдÊÖ)


ÒýÓûØÌû:
6Â¥: Originally posted by dbb627 at 2012-01-05 18:25:08:
×öͼÈçÏÂ

[ Last edited by dbb627 on 2012-1-5 at 18:30 ]

Åå·þ£¡¿ÉÒÔµÃÈ«·Ö¡£
8Â¥2012-01-05 19:40:59
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

phoenix708

Ìú¸Ëľ³æ (ÖøÃûдÊÖ)

ËÍÏÊ»¨Ò»¶ä
ÒýÓûØÌû:
Â¥: Originally posted by dbb627 at 2012-01-05 18:25:08:
×öͼÈçÏÂ

[ Last edited by dbb627 on 2012-1-5 at 18:30 ]

ºÜÀ÷º¦°¡£¬²»¹ýÕâ¸ö½á¹ûºÍÎÒÏëÒªµÄ½á¹ûÓвî¾à£¬ÎÒ¾ÀÕýÁ˵ڶþ¸öºÍµÚÈý¸ö·½³ÌµÄϵÊý£¬¿Ï¶¨ÊǶԵģ¬ÀͼݴóÏÀ×îºó°ïÎÒ¼ÆËãÒ»´Î£¡¶àл¶àл£¡
dX/dt=1.98S(1-X)-0.73XY
dY/dt=dX/dt-4.6Y/(1+Y+2S)-0.059d[Y/(1+Y+2S)]/dt
2dS/dt=-dX/dt-1.25S/(1+Y+2S)-0.086d[S/(1+Y+2S)]/dt
µ±t=0ʱ,X=0,Y=0,S=1,
ÆäÖÐ tµÄ×î´óֵΪ3£¬
ÇóX£¬Y, SÓëtµÄ¹ØÏµÍ¼
лл!
9Â¥2012-01-05 19:52:47
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû

kingslcq

гæ (ÕýʽдÊÖ)

°®¿ÆÑ§µÄPH.D & Prof.

¡¾´ð°¸¡¿Ó¦Öú»ØÌû

¸Ðл²ÎÓ룬ӦÖúÖ¸Êý +1
phoenix708(½ð±Ò+1): 2012-01-05 20:00:10
10Â¥2012-01-05 19:54:13
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
Ïà¹Ø°æ¿éÌø×ª ÎÒÒª¶©ÔÄÂ¥Ö÷ phoenix708 µÄÖ÷Ìâ¸üÐÂ
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