Logistic difference equation

The logistic difference equation displays dynamical behavior when it is iterated, that is, when its result is repeatedly "fed back" to calculate a new result. The equation is the simplest dynamical system imaginable, fully determined by a single variable or degree of freedom, 'x.' X's value at "time" n is used to calculate its result at "time" n+1.

x_n+1 = r (x_n) (1-x_n)

This equation produces stable behavior, including stable and bistable states. It also produces bifurcations, and periods of chaotic behavior. Proximity to a bifucation is detectable by examining a perturbation's effect on relaxation time.

download an Excel file to model the logistic difference equation, inserting different values for the initial conditions (x₁) and the "nonlineariry factor" (r).

---

Last updated 8-15-01 ©Dave Thompson PT