Logistic Differential Equation

Logistics differential equation. Theory and Proof. The Logistic Differential Equation. The exponential model is used to study uninhibited population growth and solution is the exponential function . When the term is added we obtain the logistic differential equation which is used to model inhibited population growth or bounded population growth. The logistic differential equation is. One form of the solution is. The terms have been carefully determined so that the initial condition is. The limiting value L of y(t) is given by. The graph is the so called "S-shaped" curve. The choice of parameters creates the curve shown below. The solution curve to the logistic differential equation.