Generalized synchronization of regulate seizures dynamics in partial epilepsy with fractional-order derivatives

The dynamical behavior and the synchronization of epileptic seizure dynamics, with fractional-order derivatives, is studied in this paper. Knowing that the dynamical properties of ictal electroencephalogram signal recordings during experiments displays complex nonlinear behaviors, we analyze the system from chaos theory point of view. Based on stability analysis, the system presents three equilibrium points with two of them unstable. Moreover, the system reveals attractor points from the phase portrait analysis. In addition, the largest Lyapunov exponent displays positive values after a given period of time. These observations characterize a chaotic behavior of epileptic seizure dynamics. Therefore, based on the Ge-Yao-Chen partial region stability theory, the synchronization of the system is achieved and simulations prove that the control technique is very efficient. Further studies based on phase synchronization show that we are able to force infected population of neurons by epilepsy into synchronization with uninfected one through a coupling constant. In addition, based on the phase locking value time evolution (phase synchronization) of the system, we realize that fractional-order derivative induces quick synchronization compared to integer order derivative. These results might be very interesting from the medical point of view, because by applying the proposed control method, one may be able to regulate (or reduce) seizure amplitude which, if kindly implemented in practice, will provide excellent therapeutic solution to drug resistant patients with epilepsy.