EEG Synthesis
On the basis of recent papers [2] and [14] describing new methods of modeling and simulation that reverse engineer dynamics, a set of EEG's were examined and the figure below constructed by a process known as Dynamical Synthesis. Sample size 65000 @100/second. Lead O1-A1.
The method of Dynamical Synthesis has been described and documented in many articles. It demonstrates that complex dynamics that cannot be modeled on the basis of first principles may still be modeled by reverse engineering the dynamics as described in the references below.

The method is as follows: We examine the EEG or EKG delay plot. From this, and our expertise in reversing engineering dynamics, we construct a simple mathematical model as described in the references below, esp [2]. We then seek to match the components of the model to the physiology that generates the EEG or EKG. We then measure these components separately in an effort to refine the parameters of the model. When the model converges we then use it to examine abnormal EEG's or EKG' s. Specifically, we are seeking to find variances in the physiological presentation of the abnormal cases from the model. These changes may then lead to understanding specific physiological processes and their evolution from normal to abnormal. The long term goal is to be able to predict seizures or sudden cardiac death well before they occur.

The figure above demonstrates that the starting point from which to develop an EEG model is the Complex Wave Equation described in [2].

[1] Brown, R., [1992] “Generalizations of the Chua Equations,” IEEE Transactions on Circuits and Systems 40(11).
[2] ]Brown, R. \& Jain, V. [2009], A New Approach to Chaos, Dynamics of Continuous, Discrete and Impulsive Systems to appear. Invited Paper
[3] Brown, R., Berezdivin, R., and Chua, L., [2001] “Chaos and Complexity”, International Journal of Bifurcation and Chaos 11(1)
[4] Chua, L., Brown, R. and Hamilton, N. [1993] ``Fractals in the Twist-and-Flip Circuit'' Proceedings of the IEEE, Invited Paper.
[5] Brown, R. \& Chua, L. [1991] "Horseshoes in the Twist-and-Flip
Map,"International Journal of Bifurcation and Chaos {\bf 1}(1),235-252.
[6] Brown, R. \& Chua, L. [1993] ``Dynamical Synthesis of
Poincar\'{e} Maps,'' International Journal of Bifurcation and Chaos {\bf 3}(5),1235-1267.
[7] Brown, R. \& Chua, L. [1996] ``Clarifying Chaos: Examples
and Counterexamples,'' International Journal of Bifurcation and Chaos {\bf 6}(2)
[8] Brown, R. and Chua, L., [1996] “From almost periodic to chaotic: The fundamental map” International Journal of Bifurcation and Chaos 6(6).
[9] Brown, R. and Chua, L., [1997] “Chaos: Generating complexity from simplicity” International Journal of Bifurcation and Chaos 7(7).
[10] Brown, R. \& Chua, L. [1998] ``Clarifying Chaos II:Bernoulli Chaos, Zero Lyapunov Exponents, and Strange
Attractors'' International Journal of Bifurcation and Chaos {\bf 8}(1), pp.1-32
[11] Brown, R. and Chua, L., [1999] "Clarifying Chaos III: Stochastic Processes" International Journal of Bifurcation and Chaos 9(5).
[12] Poincar´e, H. [1892]. Les Methodes Nouvelles de la Mechanique Celeste. Gauthier–Villars, Paris.
[13] Smale S. [1967] Differentiable Dynamical Systems. Bull Am Math Soc {\bf 73}:747–817.
[14] Brown [2009] Are we Approaching Complex Systems from the Wrong End? To be summitted to Scientific American