Nonlinear Dynamical Systems with Chaos and Big Data: A Case Study of Epileptic Seizure Prediction and Control

The modeling of dynamic behavior of systems is a ubiquitous problem in all facets of human endeavors. Importantly so, dynamical systems have been studied and modeled since the nineteenth century and currently applied in almost all branches of sciences and engineering including social sciences. The development of computers and scientific/numerical methods has accelerated the pace of new developments in modeling both linear and nonlinear dynamical systems. However, modeling complex physical system behaviors as nonlinear dynamical systems is still difficult and challenging. General approaches to solving such systems typically fail and require personalized problem dependent techniques to satisfy the constraints imposed based on the initial conditions to predict state space trajectories. In addition, they require enormous computational power available on supercomputers. Numerical tools such as HPCmatlab enable rapid prototyping of algorithms for large scale computations and data analysis. BigData applications are computationally intensive and I/O bound. An example, state of the art case study involving big data of epileptic seizure prediction and control is presented. The nonlinear dynamical model is based on the biology of the brain and its neurons, chaotic systems, nonlinear signal processing, and feedback and adaptive systems. The goal is to develop new feedback controllers for the suppression of epileptic seizures based on electroencephalographic (EEG) data by altering the brain dynamics through the use of electrical stimulation. The research is expected to contribute to new modes of treatment for epilepsy and other dynamical brain disorders.