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Update 2024-12-21-System dynamics.md
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choisunmi00 committed Dec 26, 2024
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Expand Up @@ -22,7 +22,7 @@ math: true
- 억제제: $$V_{t} = D_{v} \Delta V + a-U- \rho R(U,V)$$
- $$$$
$$R(U,V) = \frac{dUV}{e + fU + gU^{2}}$$
- 확산제와 억제제에 의해 농도와 분포가 시간에 따라 경쟁 -> 무늬(패턴) 형성
- 확산제와 억제제에 의해 농도와 분포가 시간에 따라 경쟁 무늬(패턴) 형성
## Lotka-Volterra equation
---
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- $$$$
$$\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\$$
$$= B_0 \left( 1 - \frac{D_0 N}{B_0} \right) N = r \left( 1 - \frac{N}{C} \right) N$$
$$\Rightarrow N(t) = \frac{C N_0}{N_0 + (C - N_0)e^{-rt}}$$
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