Model updating and simulation of Lyapunov exponents

We describe a control method based on optimization techniques to control of spatiotemporal chaos in a globally coupled map lattice (CML) system. We have developed a method for updating a CML model emulating complex spatial dynamics in an epileptic brain that exhibits characteristic spatiotemporal changes seen during transitions into a seizure susceptible state. Our updating algorithm uses metaheuristic techniques for obtaining feedback control parameters for controlling spatiotemporal chaos (local and global Lyapunov exponents). This methodology can be used in systems with hidden variables, i.e. where not all variables can be observed, such as the human brain, to reconstruct evolution maps and complex spatial patterns. Results from numerical simulations show that this algorithm is robust and effective in achieving controllability of the lattice model. We discuss the computational aspects of this learning methodology and its potential application in epileptic seizure control.