title: Adaptive Fractional-order Control for Synchronization of Two Coupled Neurons in the External Electrical Stimulation.
abstract: This paper addresses synchronizing two coupled chaotic FitzHugh-Nagumo (FHN) neurons with weakly gap junction under external electrical stimulation (EES). To transmit information among coupled neurons, by generalization of the integer-order FHN equations of the coupled system into the fractional-order in frequency domain using Crone approach, the behavior of each coupled neuron relies on its past behavior and the memorized system can be a better fit for the neuron response. An adaptive fractional-order controller based on the Lyaponuv stability theory was designed to synchronize two neurons electrically coupled with gap junction in EES. The proposed controller is also robust to the inevitable random noise such as disturbances of ionic channels. The simulation results demonstrate the effectiveness of the control scheme.
authors.affiliation: Electrical Engineering Department, Iran University of Science and Technology, IUST, Tehran, Iran.
authors.forename: M R Rahmani
authors.initials: MR
authors.lastname: Mehdiabadi
authors.affiliation: Biomedical Engineering Department, Iran University of Science and Technology (IUST), Tehran, Iran.
authors.forename: E
authors.initials: E
authors.lastname: Rouhani
authors.affiliation: Electrical Engineering Department, Iran University of Science and Technology, IUST, Tehran, Iran.
authors.forename: S K Mousavi
authors.initials: SK
authors.lastname: Mashhadi
authors.affiliation: Electrical Engineering Department, Iran University of Science and Technology, IUST, Tehran, Iran.
authors.forename: A A
authors.initials: AA
authors.lastname: Jalali
keywords: Fractional-Order; Lyaponuv Function; Neuron Model; Synchronization