5,857 research outputs found
Chaos synchronization of the master-slave generalized Lorenz systems via linear state error feedback control
This paper provides a unified method for analyzing chaos synchronization of
the generalized Lorenz systems. The considered synchronization scheme consists
of identical master and slave generalized Lorenz systems coupled by linear
state error variables. A sufficient synchronization criterion for a general
linear state error feedback controller is rigorously proven by means of
linearization and Lyapunov's direct methods. When a simple linear controller is
used in the scheme, some easily implemented algebraic synchronization
conditions are derived based on the upper and lower bounds of the master
chaotic system. These criteria are further optimized to improve their
sharpness. The optimized criteria are then applied to four typical generalized
Lorenz systems, i.e. the classical Lorenz system, the Chen system, the Lv
system and a unified chaotic system, obtaining precise corresponding
synchronization conditions. The advantages of the new criteria are revealed by
analytically and numerically comparing their sharpness with that of the known
criteria existing in the literature.Comment: 61 pages, 15 figures, 1 tabl
The stability of adaptive synchronization of chaotic systems
In past works, various schemes for adaptive synchronization of chaotic
systems have been proposed. The stability of such schemes is central to their
utilization. As an example addressing this issue, we consider a recently
proposed adaptive scheme for maintaining the synchronized state of identical
coupled chaotic systems in the presence of a priori unknown slow temporal drift
in the couplings. For this illustrative example, we develop an extension of the
master stability function technique to study synchronization stability with
adaptive coupling. Using this formulation, we examine local stability of
synchronization for typical chaotic orbits and for unstable periodic orbits
within the synchronized chaotic attractor (bubbling). Numerical experiments
illustrating the results are presented. We observe that the stable range of
synchronism can be sensitively dependent on the adaption parameters, and we
discuss the strong implication of bubbling for practically achievable adaptive
synchronization.Comment: 21 pages, 6 figure
Using discrete-time hyperchaotic-based asymmetric encryption and decryption keys for secure signal transmission
In this paper, a framework for the synchronization of two non-identical discrete-time hyperchaotic systems, namely the 3D Baier-Klein and the 3D Hitzel-Zele maps, based on the use of hybrid output feedback concept and aggregation techniques, is employed to design a two-channel secure communication system. New sufficient conditions for synchronization are obtained by the use of Borne and Gentina practical criterion for stabilization study associated to the forced arrow form matrix for system description. The efficiency of the proposed approach to confidentially recover the transmitted message signal is shown via an application to the hyperchaotic Baier-Klein and Hitzel-Zele systems, considered as generators of asymmetric encryption and decryption keys
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