From e6552551376aa74bcc870a74be61ac4258e5218e Mon Sep 17 00:00:00 2001 From: choisunmi00 Date: Thu, 26 Dec 2024 18:40:29 +0900 Subject: [PATCH] Update 2024-12-21-System dynamics.md --- _posts/2024-12-21-System dynamics.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/_posts/2024-12-21-System dynamics.md b/_posts/2024-12-21-System dynamics.md index 3a084f6..397da1a 100644 --- a/_posts/2024-12-21-System dynamics.md +++ b/_posts/2024-12-21-System dynamics.md @@ -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}}$$ -- 확산제와 억제제에 의해 농도와 분포가 시간에 따라 경쟁 -> 무늬(패턴) 형성 +- 확산제와 억제제에 의해 농도와 분포가 시간에 따라 경쟁 ⟶ 무늬(패턴) 형성 ## Lotka-Volterra equation --- @@ -40,7 +40,7 @@ math: true - $$$$ $$\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\$$ + $$= B_0 \left( 1 - \frac{D_0 N}{B_0} \right) N = r \left( 1 - \frac{N}{C} \right) N$$ $$\Rightarrow N(t) = \frac{C N_0}{N_0 + (C - N_0)e^{-rt}}$$ 1