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Abstract
With comprehensive consideration of generalized synchronization, combination synchronization and adaptive control, this paper investigates a novel adaptive generalized combination complex synchronization (AGCCS) scheme for different real and complex nonlinear systems with unknown parameters. On the basis of Lyapunov stability theory and adaptive control, an AGCCS controller and parameter update laws are derived to achieve synchronization and parameter identification of two real drive systems and a complex response system, as well as two complex drive systems and a real response system. Two simulation examples, namely, ACGCS for chaotic real Lorenz and Chen systems driving a hyperchaotic complex Lü system, and hyperchaotic complex Lorenz and Chen systems driving a real chaotic Lü system, are presented to verify the feasibility and effectiveness of the proposed scheme.
Highlights
Since Pecora and Carrol firstly investigated synchronization in chaotic systems in 1990,1 chaos synchronization has attracted continuous attention and been a hot interdisciplinary topic of natural science, engineering and social science, due to its extensively potential applications in the fields of secure communication, control and signal processing, neural networks, bioengineering, etc
With comprehensive consideration of generalized synchronization, combination synchronization and adaptive control, this paper investigates a novel adaptive generalized combination complex synchronization (AGCCS) scheme for different real and complex nonlinear systems with unknown parameters
For the given complex mapping vectors φ(u) and ψ(v), the real response system (15) can be synchronized with the complex drive system (13) and (14) in sense of AGCCS asymptotically, and the estimated values of unknown parameters converge to their true values, if the real adaptive controller and update laws of the unknown parameters are designed as: L(u, v, w) = −s(w) + Jr(φ)pr(u) − Ji(φ)pi(u) + Jr(ψ)qr(v) − Ji(ψ)qi(v) +[Jr(φ)Pr(u) − Ji(φ)Pi(u)]θ + [Jr(ψ)qr(v) − Ji(ψ)qi(v)]ξ − S(w)δ − K e θξ ̇ ̃
Summary
Since Pecora and Carrol firstly investigated synchronization in chaotic systems in 1990,1 chaos synchronization has attracted continuous attention and been a hot interdisciplinary topic of natural science, engineering and social science, due to its extensively potential applications in the fields of secure communication, control and signal processing, neural networks, bioengineering, etc. To solve this problem, Luo et al proposed a combination synchronization scheme for synchronizing a chaotic response system with two chaotic drive systems.[20] Since combination synchronization has achieved some new developments. There are two problems to be addressed: one is shall we further generalize these synchronization schemes to synchronize nonlinear systems with respect to a given complex functional relationship; the other is how to realize combination synchronization and parameter identification for real and complex nonlinear systems with unknown parameters.
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