Nonlinear Science
© 2013 EEASI Corporation


Nonlinear science is the study of highly complex systems whose long-term predictability is similar to a random process. In the most extreme cases, nonlinear systems are as random as a coin toss.; this is known as chaos.

The essential feature of chaos is that, theoretically, with perfect knowledge of the initial conditions(starting points), the system is predictable. However, perfect knowledge is not attainable and as a result, even a small error in the measurement of the initial conditions will produce an outcome that is uncorrelated to the dynamics of the system given perfect measurements. Also, the future of even an imperfectly measured system will become uncorrelated with is past.

Subchaos is a class of complex systems which are not chaotic in the sense of the Smale-Birkhoff Theorem but are never the less complex. The surprising nature of these systems is that they are "almost periodic". If one thinks of a periodic system as the most predictable system, then an almost periodic system should not be too for off from predictable. However, this is not true as the link on subchaos shows: Almost periodic systems can be astoundingly complex.

Almost periodic chaos is yet another class of complex dynamical systems. We know that autonomous nonlinear systems, when driven by periodic forcing produce chaos. But what if the forcing is almost periodic? Almost periodic forcing is far more natural than periodic forcing, which is just an idealized form of dynamics. Hence the study of almost periodically forced system would be very valuable. In the link on almost periodic chaos we present a "time-one" plot showing how the "chaotic" dimension of the system drifts in a way that can resemble true dynamics of the human EEG..