Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen–Lee systems

Abstract

Recently, the fractional-order Chen-Lee system was proven to exhibit chaos by the presence of a positive Lyapunov exponent. However, the existence of chaos in fractional-order Chen-Lee systems has never been theoretically proven in the literature. Moreover, synchronization of chaotic fractional-order systems was extensively studied through numerical simulations in some of the literature, but a theoretical analysis is still lacking. Therefore, we devoted ourselves to investigating the theoretical basis of chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen-Lee systems in this paper. Based on the stability theorems of fractional-order systems, the necessary conditions for the existence of chaos and the controllers for hybrid projective synchronization were derived. The numerical simulations show coincidence with the theoretical results.

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

“…Yet, several authors are also interested in the synchronization of the fractional-order a e-mail: g.litak@pollub.pl chaotic systems [22,23,[26][27][28][29][30][31][32][33][34][35]. The transient time preceding the synchronization state of chaotic oscillators is crucial as it unfortunately corresponds to the laps of time during which the encoded message cannot be recovered or sent.…”

Chaos synchronization in fractional differential systems

“…Meanwhile, based on the stability of fractional differential systems, HPS of commensurate and incommensurate fractional Chen-Lee chaotic systems was studied by Chang & Chen [91], by designing a nonlinear controller. Using a specific state variable and its time derivatives, a new HPS scheme was also presented and applied to three-dimensional fractional unified chaotic systems by Chang & Chen [91].…”

“…Using a specific state variable and its time derivatives, a new HPS scheme was also presented and applied to three-dimensional fractional unified chaotic systems by Chang & Chen [91].…”

Synchronization of fractional‐order chaotic systems with disturbances via novel fractional‐integer integral sliding mode control and application to neuron models

“…Control and synchronization of chaotic systems are very important topics to research in science and engineering. Many techniques have been presented for chaos control and chaos synchronization of fractional‐order systems . One of the significant nonlinear control approaches is the sliding mode control.…”