Sensitive dependence is a characteristics of +feedback growth processes because their current states depend critically on their initial, or starting, states. We can prove this as follows: Suppose we have a population of N₀ individuals with a constant rate of change, R, and we wish to predict its growth into the future. However, suppose that our estimate of the density of the population has a small error, x₀. The true population will grow according to the equation N_t = N₀e^Rt while the predicted population will grow according to the equation

E[N_t] = (N₀ - x₀)e^Rt,

and the difference between real and predicted population will be:

which shows that the error, x₀, or the difference in the real and estimated initial condition, is amplified exponentially with time for values of R > 0. Because of the fact that errors are magnified with time, and other reasons, sensitivity to initial conditions is an extremely important property of population systems.

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