Complexity Explorer Santa Fe Institute


Lyapunov exponent

The Lyapunov exponent is a value that describes the rate at which two nearly identical trajectories within a dynamic system's phase space will separate from one another per unit of time. It is indicative of a system's sensitivity to initial conditions:  a large Lyapunov will reflect a system in which a very small perturbation of the system will cause a large change in the trajectory of the system within its phase space. 

For N-dimensional systems, there will be N Lyapunov exponents, one that measures the rate of separation along each dimension.  The largest of these is called the "maxiumal Lyapunov exponent" or MLE.  A positive MLE is one indicator that a system is chaotic. 


Topics
Chaos, Mathematics, Nonlinear Dynamics, Statistical Physics
Difficulty
1