Novel results on projective synchronization of fractional-order neural networks with multiple time delays. (December 2018)

• Record Type: Journal Article
• Authors: Zhang, Weiwei; Cao, Jinde; Wu, Ranchao; Chen, Dingyuan; Alsaadi, Fuad E.
• Is Part Of: Chaos, solitons and fractals. Volume 117(2018)
• Page Start: 76
• Page End: 83
• Publication Date: 2018-12
• Subjects: Fractional order neural networks -- Multiple time delays -- Projective synchronization; 26A33 -- 92B20 -- 94B50; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2018.10.009
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: The main contributions of this paper lies in three aspects. First, multiple time delays are taken into account. Hence, a new hybrid controller is designed to achieve the projective synchronization of FONN with multiple time delays, and this is a key contribution since the linear controllers in previous literatures [24, 30] could not solve the projective synchronization of FONN. Second, based on the stability theorem of linear fractional order systems with multiple delays and comparison principle, two new synchronization conditions of FONN with multiple time delays are proposed here. Moreover, the finding results can be used to realize the complete synchronization and anti-synchronization. Finally, in comparison with previous works [20, 21], our results contain time delays and achieve a valuable improvement, giving quit confidence to say that the results obtained in this letter are less conservative and more general. Abstract: This paper investigates a projective synchronization of fractional-order neural networks (FONN) with multiple time delays, and two new synchronization conditions are derived by combining open loop control and linear control. This is achieved by employing stability theorem of linear fractional order systems with multiple delays and comparison principle. Feasibility of the theoretical results is validated through numerical simulations.