Much of theoretical and empirical economics is based on adaptations of linear differential and difference equations. While fine up to a point, there is no compelling reason to think that linear equations are adequate.
Nonlinear dynamics offers an alternative to using linear equations to describe sequences.
Advances in the 1980s and 1990s indicated that nonlinear equations can generate much more complicated response patterns than can linear equations. Chaos theory itself involves generating seemingly random outcomes from deterministic sequences. Chaos theory is not particularly informative in economics. Nonlinear time series analysis, on the other hand, can be extremely informative about aspects of the economy. Nonlinear time series can have much more complicated responses of the economy to shocks.