Nonlinear difference equation

Summary

A nonlinear difference equation is a recurrence relation in which the next term is not an affine function of the earlier terms. Products, powers, quotients or other nonlinear functions of the earlier terms may appear. Unlike linear recurrences, such equations rarely have closed-form solutions, and their solutions can converge, oscillate, or behave chaotically. They model population dynamics, iterative numerical methods and many discrete-time systems.