Phase distribution control of neural oscillator populations using local radial basis function meshfree technique with application in epileptic seizures: A numerical simulation approach

Abstract

Since control of synchronization at the onset of seizure can be considered an effective method of preventing or treating epilepsy, developing an advanced and accurate numerical simulation approach to implement control on noise-free (or noisy) population of synchronized neurons makes the control performance more effective. In this paper, we simulate a control by two powerful, fast and accurate meshless methods, i.e. compactly supported radial basis function collocation (CS-RBF) and radial basis function generated finite difference (RBF-FD) approaches, which enable us to realize new control objectives. It should be noted that the challenges faced by this model include the diverse behavior of neuronal populations, the speed of action in synchronization control, the minimization of energy consumption and the applicability of controlling real data, we show that the both proposed meshfree methods solve all these challenges. In addition, the evaluation of both methods by different phase response curves (PRC) as well as in the presence of Gaussian white noise shows that these methods can be implemented in experimental cases. The analyses and numerical results presented eventually confirm these claims.