Logistic ODE Euler Step

Problem

Take one explicit Euler step for the logistic ODE y' = r * y * (1 - y / k), where r is the growth rate and k is the carrying capacity.

Given the current population y and step size dt, return y + dt * r * y * (1 - y / k). Assume k != 0.

Hint

At y = 0 and y = k the growth term is zero, so the state does not move.

case 1

in: [1,1,10,0.5]

expected: 1.45

case 2

in: [5,0.2,10,1]

expected: 5.5

case 3

in: [0,1,10,0.5]

expected: 0

case 4

in: [10,1,10,0.5]

expected: 10

case 5

in: [2,-1,10,0.5]

expected: 1.2

Starter codePython

def logistic_euler_step(y, r, k, dt):
    # Your code here
    pass

5 test cases · run your code against them in the editor