Complexity Explorer Santa Fe Institute

logistic map

The logistic map is the simple recurrence relation: x_(n + 1) = x_n * R * ( 1 - x_n ), which produces chaotic behavior under certain parameters .  

This map is a version of Verhulst's logistic model of population growth, where x_n represents the population (as a fraction of carrying capacity) at time n, and R is the growth rate.  In order to keep x_n between 0 and 1, R is restricted to be between 0 and 4. 

Nonlinear Dynamics, Chaos, Dynamical Systems, Statistical Physics