Generalized Combination Complex Synchronization for Fractional-Order Chaotic Complex Systems

Abstract

Based on two fractional-order chaotic complex drive systems and one fractional-order chaotic complex response system with different dimensions, we propose generalized combination complex synchronization. In this new synchronization scheme, there are two complex scaling matrices that are non-square matrices. On the basis of the stability theory of fractional-order linear systems, we design a general controller via active control. Additionally, by virtue of two complex scaling matrices, generalized combination complex synchronization between fractional-order chaotic complex systems and real systems is investigated. Finally, three typical examples are given to demonstrate the effectiveness and feasibility of the schemes.

Synchronization and antisynchronization of N‐coupled fractional‐order complex chaotic systems with ring connection

“…Meanwhile, many interesting and important results on synchronization of the fractional‐order complex chaotic systems are also obtained. For example, Jiang et al explored generalized combination complex synchronization for fractional‐order complex chaotic systems. A bridge between the fractional‐order complex chaos and real hyperchaos was built in Liu by investigating complex modified hybrid projective synchronization.…”

A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos

“…Now, it is well-known that many real-world physical systems [1][2][3][4] can be more accurately described by fractional-order differential equations, for example, dielectric polarization, viscoelasticity, electrode-electrolyte polarization, electromagnetic waves, diffusion-wave, superdiffusion, heat conduction. Meanwhile, chaotic behavior has been found in many fractional-order systems like the fractional-order brushless DC motor chaotic system [5,6], the fractional-order gyroscopes chaotic system [7], the fractional-order microelectromechanical chaotic system [8], the fractional-order electronic circuits [9,10], and so forth [11][12][13][14][15][16].…”

Adaptive generalized combination complex synchronization of uncertain real and complex nonlinear systems

“…22 Noticeably, Jiang et al proposed combination complex synchronization of chaotic real systems and complex systems with different dimensions via two complex scaling matrices. 23 As introduced in Refs. [24][25][26][27][28], synchronization between chaotic real and complex systems can offer more options of chaotic generators for secure communication and digital cryptography, which can increase the difficulty to decrypt and decipher the encrypted signals and information.…”