0f0919eb-96be-4123-8fab-b7621fb6fbc3 2 4 5 false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

DE Verhulst [Logistic]

a k r t0 Clear 1

a k t f 1 y a y - (* / y int k t int ≡ y solve maple :

a k t f a k t * a * exp * 1 - k t * a * exp + /

a k t f a k t * a * exp * 1 k t * a * exp + / :

a k y0 t f1 1 u a u - (* / u y0 y int k u 0 t int ≡ y solve maple :

a k y0 t f1 y0 a * k t * a * exp * a y0 1 - k t * a * exp + (* + /

a k y0 t f1 y0 a * k t * a * exp * a y0 1 - k t * a * exp + (* + / :

k y0 t0 t f2 1 u 1 u - (* / u y0 y int k u t0 t int ≡ y solve maple :

k y0 t0 t f2 y0 k t t0 - (* exp * 1 y0 1 - k t t0 - (* exp + (* + /

yo r t to - (* exp * 1 yo - yo r t to - (* exp * + / 111 yo / 1 - (r t to - (* - exp * + / ≡

NOT from Smath

a k y0 t0 t f3 1 u a u - (* / u y0 y int k u t0 t int ≡ y solve maple :

a k y0 t0 t f3 y0 a * k a * t t0 - (* exp * a y0 1 - k a * t t0 - (* exp + (* + /

r to yo t Logistic 111 yo / 1 - (r t to - (* - exp * + / :

yo yo - 1 + (r t to - (* - exp * + yo /

a k y0 t f1 y0 a * k t * a * exp * a y0 1 - k t * a * exp + (* + / :

r 1 : yo 0.5 : to 0 : ε 1.5 : 14 mat

a k t f a k t * a * exp * 1 k t * a * exp + / :

r to yo x Logistic r to ε - yo x Logistic r to ε + yo x Logistic to yo . 15 blue 1 5 mat 4 1 sys 1.25 0.5 x f 1.25 0.75 x f 1.25 1 x f 3 1 sys 1.25 0.5 0.025 x f1 1.25 0.75 0.025 x f1 1.25 1 0.025 x f1 3 1 sys