Global optimization approaches to reconstruction of dynamical systems related to epileptic seizures

The complex chaotic, unstable, noisy and nonlinear dynamics of the brain requires alternative approaches to identification and simulation of brain activity. These approaches differ from the universally accepted stochastic simulation of random processes with a given distribution. In this report we discuss the possibility of using a global optimization approach to the reconstruction of brain dynamics under the assumption that the diagnostic information comes in the form of a nonlinear time series. We consider a method for global reconstruction of nonlinear models for systems where all the necessary variables have not been observed. This technique can be applied to systems with one or several such hidden variables, and can be used to reconstruct maps or differential equations of brain dynamics. The quadratic programing approach to reconstruction of dynamical process is considered. We propose the possibility of the global reconstruction of the Fokker - Planck equation for a multi-variable distribution function which re ects the complexity of the considered brain. Finally, we demonstrate an application of the reconstructing technique to the analysis of a complex noisy system.