An example of a nonlinear discrete dynamic system
F : Xn+1 = 4 Xn ( 1 - Xn )
Let X1o = 0.43555 and X2o = 0.43556 be the initial conditions of two systems following the
same map F
The plots of these two systems as a function of n:
Note that, even though the initial values differ by a very small amount, the systems diverge from each other as iterations(n) increase.
The histogram of X1, X2 and abs(X1-X2) is shown below.
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Now you can experiment with a general system
: Xn+1 = Growth_rate * Xn ( 1 - Xn )
A single dimensional random walk problem simulation
Let Xn+1 = Xn + dx
Where dx is a random variable with the possible values (1,-1) and n is the step count.
Click the button to see the simulation of this system for 200 steps.