Adaptive Synchronization Strategy between Two Autonomous Dissipative Chaotic Systems Using Fractional-Order Mittag–Leffler Stability

Abstract

Compared with fractional-order chaotic systems with a large number of dimensions, three-dimensional or integer-order chaotic systems exhibit low complexity. In this paper, two novel four-dimensional, continuous, fractional-order, autonomous, and dissipative chaotic system models with higher complexity are revised. Numerical simulation of the two systems was used to verify that the two new fractional-order chaotic systems exhibit very rich dynamic behavior. Moreover, the synchronization method for fractional-order chaotic systems is also an issue that demands attention. In order to apply the Lyapunov stability theory, it is often necessary to design complicated functions to achieve the synchronization of fractional-order systems. Based on the fractional Mittag–Leffler stability theory, an adaptive, large-scale, and asymptotic synchronization control method is studied in this paper. The proposed scheme realizes the synchronization of two different fractional-order chaotic systems under the conditions of determined parameters and uncertain parameters. The synchronization theory and its proof are given in this paper. Finally, the model simulation results prove that the designed adaptive controller has good reliability, which contributes to the theoretical research into, and practical engineering applications of, chaos.

A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit

“…Observing the state of the variable phase diagrams or time domain graphs of the system, we can find that the state variables w and u are beyond the linear range of the integrated amplifiers. Therefore, the variable compression processing is required using Equation (8). After compression, system (3) becomes Equation (9).…”

“…Since the discovery of the first chaotic attractor by meteorological scientist Lorenz in 1963 [1], scholars have continued to research and explore new chaotic systems composed of ordinary differential equations. The most representative ones are three-dimensional continuous chaotic systems represented by autonomous ordinary differential equations, such as the Lü system [2,3], Rössler system [4], Chen system [5], and some other typical chaotic systems [6][7][8][9][10][11]. Various four-dimensional chaotic systems or hyperchaotic systems can be obtained by adding linear or nonlinear state feedback controllers based on three-dimensional chaotic systems [12][13][14].…”

A new approach for security of wireless sensor networks based on anti-synchronization of the fractional-order hyper-chaotic system

“…Several methods have been used in secure communications. The various methods that have been presented for synchronization include active control (Huang and Cao, 2017), impulse control (Stamov and Stamova, 2017), sliding mode control (Rabah et al, 2017), back-stepping control (Shukla and Sharma, 2017), adaptive control (Liu et al, 2019), and robust control (Khanzadeh and Pourgholi, 2016).…”

Complex Modified Projective Synchronization of Fractional-Order Complex-Variable Chaotic System with Unknown Complex Parameters

“…Meanwhile, chaotic dynamics and synchronization of fractional-order nonlinear systems have aroused tremendous attention of many researchers. Many excellent results have been obtained and some types of synchronization have been presented [ 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]. In various synchronizations, modified projective synchronization (MPS) refers to the master system and slave system being synchronized to a constant scaling diagonal matrix.…”