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Q 14: Logistic Equation - Coggle Diagram
Q 14: Logistic Equation
Applications
Biology
Identifying animal and plants population growth
Modeling crop response
Medicine
Modeling the growth of tumors
Modeling of a pandemic and predicting peaks of contamination
Sociology
illustrate the progress of the diffusion of an innovation of some kind
Mathematics and statistic
Machine learning
Logistic regression
Neural networks
Standard Logistic Function
parameters
k=1
x0 = 0
L=1
Also called Sigmoid
Logistic Diferrential Equation
dP/dT = kP(1 - P/L)
P = population at time t
L = max size of populaiton
k = constant of proporcionality
Predict population growth
Thomas Malthus
Pierre Verhulst
ODE
non-linear
Solution
P(t) = P0*k / ((k - P0) exp(-rt) + P0)
P(t) => k, when t goes to infinity
Inflection point
Second derivative
Sigmoid function
