Abstract
In this paper, a new hyperchaotic complex system is presented and its dynamical properties are discussed by phase portraits, bifurcation diagrams, and the Lyapunov exponents spectra. Noticeably, based on two drive complex systems and one response complex system with different dimensions, we propose generalized combination complex synchronization and design a general controller. Additionally, we investigate generalized combination complex synchronization between real systems and complex systems via two complex scaling matrices. Two examples, which include two chaotic complex systems driving one new hyperchaotic complex system and two new hyperchaotic complex systems driving one chaotic real system, are shown to demonstrate the effectiveness and feasibility of the schemes.
Highlights
In, Fowler et al [ ] proposed the complex Lorenz equations, which is the pioneering work in the domain of complex systems
Chaotic and hyperchaotic complex systems have been extensively studied owing to their important applications in physical systems, image processing and in particular in secure communication [ – ]
Inspired by the above discussion, we introduce a new hyperchaotic complex system to investigate generalized combination complex synchronization between two drive complex systems and one response complex system with different structures
Summary
In , Fowler et al [ ] proposed the complex Lorenz equations, which is the pioneering work in the domain of complex systems. Since complex variables increase the diversity and the security of the transmitted signals, these synchronization methods of chaotic complex systems have potential applications in secure communication and image processing. Sun et al [ ] investigated combination complex synchronization between two drive chaotic complex systems and one response chaotic complex system These synchronization schemes occur in chaotic complex systems with the same dimensions. To the best of our knowledge, there are few papers discussing combination synchronization among two drive systems and one response system with different dimensions in the complex space. Inspired by the above discussion, we introduce a new hyperchaotic complex system to investigate generalized combination complex synchronization between two drive complex systems and one response complex system with different structures. 2.1 Symmetry and invariance Note that the symmetry of system ( ): It is symmetric about the m -axis, which means it is invariant for the coordinate transformation of (m , m , m , m , m , m ) → (–m , –m , –m , –m , m , –m )
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