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Update 2024-12-21-System dynamics.md
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choisunmi00 committed Dec 26, 2024
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7 changes: 3 additions & 4 deletions _posts/2024-12-21-System dynamics.md
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Expand Up @@ -32,17 +32,16 @@ math: true
$$\frac{dN}{dt} = kN \Rightarrow N(t) = N_0 e^{kt}$$
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<img src="https://i.ibb.co/0Q04w6h/image.webp" alt="1" width="100%" height="100%"/>


#### 로지스트형 모델: 환경수용적 고려 모델
- $$$$
$$\frac{dN}{dt}$$
$$= (B - D)N = (B_0 - D_0 N)N$$
$$= B_0 \left( 1 - \frac{D_0 N}{B_0} \right) N = r \left( 1 - \frac{N}{C} \right) N$$
$$\Rightarrow N(t) = \frac{C N_0}{N_0 + (C - N_0)e^{-rt}}$$
<img src="https://i.ibb.co/xfDBbHD/image.webp" alt="1" width="40%" height="40%"/>
$$= B_0 \left( 1 - \frac{D_0 N}{B_0} \right) N = r \left( 1 - \frac{N}{C} \right) N\ \Rightarrow N(t) = \frac{C N_0}{N_0 + (C - N_0)e^{-rt}}$$
<img src="https://i.ibb.co/xfDBbHD/image.webp" alt="1" width="100%" height="100%"/>
<!-- ![Light mode only](https://i.ibb.co/xfDBbHD/image.webp){: .light }
![Dark mode only](https://i.ibb.co/x3hpRwz/image.png){: .dark } -->
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