0
10
20
30
40
50
60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
t
1/(1+91/9 exp(-1/10 t))
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.005
0.01
0.015
0.02
0.025
寰垎鏂圭▼寤烘ā锛堜紶鏌撶梾妯″瀷锛夌殑姹傝В銆?/p>
1
銆佹ā鍨?/p>
1
锛?/p>
SI
妯″瀷銆?/p>
鍋囪锛?/p>
锛?/p>
1
锛?/p>
t
鏃跺埢浜虹兢鍒嗕负鏄撴劅鑰咃紙鍗犳�讳汉鏁版瘮渚嬬殑
(
)
s
t
锛夊拰宸叉劅鏌撹�咃紙鍗犳�讳汉鏁版瘮渚嬬殑
(
)
y
t
锛?/p>
锛?/p>
2
锛夋瘡涓梾浜烘瘡澶╂湁鏁堟帴瑙︾殑骞冲潎浜烘暟鏄父鏁?/p>
飦?/p>
锛?/p>
飦?/p>
绉颁负鏃ユ帴瑙︾巼锛屽綋鍋ュ悍鑰呬笌鐥呬汉鎺ヨЕ
鏃讹紝鍋ュ悍鑰呭彈鎰熸煋鎴愪负鐥呬汉銆?/p>
鍒嗘瀽锛氭牴鎹亣璁撅紝姣忎釜鎮ｈ�呮瘡澶╁彲浠ヤ娇
(
)
s
t
飦?/p>
涓仴搴疯�呭彉涓虹梾浜猴紝鍥犱负鐥呬汉鏁颁负
(
)
Ny
t
锛屾墍
浠ユ瘡澶╁叡鏈?/p>
(
)
(
)
Ns
t
y
t
飦?/p>
涓仴搴疯�呭彉涓虹梾浜恒�傚嵆锛?/p>
dy
N
Nsy
dt
飦?/p>
飥?/p>
锛屼笖
(
)
(
)
1
s
t
y
t
飥?/p>
飥?/p>
锛岃鍒濆鏃跺埢鐥呬汉姣斾緥涓?/p>
b
锛屽垯锛?/p>
(1
)
(0)
dy
y
y
dt
y
b
飦?/p>
飪?/p>
飥?/p>
飥?/p>
飪?/p>
飪?/p>
飪?/p>
飥?/p>
飪?/p>
锛?/p>
鐢?/p>
MATLAB
瑙ｆ寰垎鏂圭▼锛?/p>
>> syms a b
>> f=dsolve('Dy=a*y*(1-y)','y(0)=b','t')
f =
1/(1-exp(-a*t)*(-1+b)/b)
%
1
1
(
)
1
1
1
1
(
1)
t
t
y
t
b
e
e
b
b
飦?/p>
飦?/p>
飥?/p>
飥?/p>
飥?
飥?
飥?/p>
飥?/p>
飥?/p>
飥?/p>
褰?/p>
0.09,
0.1
b
飦?/p>
飥?/p>
飥?/p>
鏃?/p>
锛?/p>
鍒?/p>
鍒?/p>
鍦?/p>
鍧?/p>
鏍?/p>
绯?/p>
oty
涓?/p>
浣?/p>
鍑?/p>
(
)
y
t
鐨?/p>
鍥?/p>
鍍?/p>
锛?/p>
鍧?/p>
鏍?/p>
绯?/p>
oyy
飩?/p>
涓?/p>
浣?/p>
鍑?
(1
)
y
y
y
飦?/p>
飩?/p>
飥?/p>
飥?/p>
鐨勫浘鍍忥紝
>> a=0.1;
>> b=0.09;
>> h=dsolve('Dy=a*y*(1-y)','y(0)=b','t')
h =
1/(1-exp(-a*t)*(-1+b)/b)
>> f=subs(h)
f =
1/(1+91/9*exp(-1/10*t))
(
)
y
t
鐨勫浘鍍?/p>
>> ezplot(f,[0,60])
>> grid on
>> figure (2)
>> fplot('0.1*y*(1-y)',[0,1])
>> grid on