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Synchronization of fractional‐order chaotic systems with disturbances via novel fractional‐integer integral sliding mode control and application to neuron models.

Authors :
Vafaei, Vajiheh
Kheiri, Hossein
Akbarfam, Aliasghar Jodayree
Source :
Mathematical Methods in the Applied Sciences; 5/30/2019, Vol. 42 Issue 8, p2761-2773, 13p
Publication Year :
2019

Abstract

In this paper, a novel fractional‐integer integral type sliding mode technique for control and generalized function projective synchronization of different fractional‐order chaotic systems with different dimensions in the presence of disturbances is presented. When the upper bounds of the disturbances are known, a sliding mode control rule is proposed to insure the existence of the sliding motion in finite time. Furthermore, an adaptive sliding mode control is designed when the upper bounds of the disturbances are unknown. The stability analysis of sliding mode surface is given using the Lyapunov stability theory. Finally, the results performed for synchronization of three‐dimensional fractional‐order chaotic Hindmarsh‐Rose (HR) neuron model and two‐dimensional fractional‐order chaotic FitzHugh‐Nagumo (FHN) neuron model. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
01704214
Volume :
42
Issue :
8
Database :
Complementary Index
Journal :
Mathematical Methods in the Applied Sciences
Publication Type :
Academic Journal
Accession number :
135990021
Full Text :
https://doi.org/10.1002/mma.5548