‎S‎ynchronization ‎of‎ different ‎dimensions‎ ‎fractional-‎order chaotic ‎systems with uncertain‎‎ ‎ parameters ‎and ‎secure ‎communication‎‎‎‎‎

Abstract

In ‎this ‎paper, ‎an‎ adaptive ‎modified‎ function projective synchronization (‎AM‎FPS) ‎scheme‎ ‎of ‎different ‎dimensions‎‎ ‎fractional-‎order ‎chaotic systems with ‎fully ‎unknown parameters is ‎presented‎. ‎On the basis of ‎fractional‎ Lyapunov stability ‎theory ‎and adaptive control law‎,‎ a‎ ‎new‎ fractional-order controller ‎and‎ suitable ‎‎‎‎update ‎rules‎ for unknown parameters are ‎designed‎‎ to realize the ‎AMFPS‎ of different ‎fractional-‎order chaotic systems with ‎non-‎identical ‎orders ‎and different dimensions‎‎. ‎‎Theoretical analysis and numerical simulations are given to verify the validity ‎of ‎the proposed ‎method. ‎Additionally, ‎‎‎‎synchronization results ‎are applied to secure communication via ‎‎ ‎modified ‎‎‎‎masking ‎method. Due to the unpredictability of the scale ‎function ‎matrix‎ and ‎using‎ of ‎fractional-‎order ‎systems with different ‎dimensions ‎and ‎u‎nequal‎ ‎orders,‎‎ the proposed scheme has higher ‎security‎‎. The security analysis ‎‎‎demonstrate that the proposed algorithm ‎has ‎a large key space ‎and‎ high sensitivity to encryption keys ‎and it is ‎‎re‎sistance to all kind of ‎‎attacks‎.

Mathematical analysis of a fractional-order predator-prey network with feedback control strategy

“…Scholars discovered that physical phenomena in nature can be depicted more accurately by fractional-order models in comparison with classical integer-order ones [8]. Recently, quite a few researchers introduced fractional calculus into the predator-prey model and constructed fractional predator-prey models, for example, design and control of various ecological models [9][10][11], secure communication [12,13], system control [14,15], and so on. Furthermore, modelling and control based on the theory of the fractional calculus of complex systems can greatly enhance the capability of discrimination, design, and control for dynamic models since fractional calculus possesses infinite memory and more degrees of freedom [16].…”