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

Abstract

Abstract. The problem of finite-time synchronization of fractional-order simplest two-component chaotic oscillators operating at high frequency and application to digital cryptography is addressed. After the investigation of numerical chaotic behavior in the system, an adaptive feedback controller is designed to achieve the finite-time synchronization of two oscillators, based on the Lyapunov function. This controller could find application in many other fractional-order chaotic circuits. Applying synchronized fractionalorder systems in digital cryptography, a well secured key system is obtained. Numerical simulations are given to illustrate and verify the analytic results.

Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form

“…By comparing with analytical time of synchronization obtained above, it can be noted that syn ≤ 1 syn . This result respects the finite-time condition given in [42]. Thus, these results can be used for chaos based communications.…”

“…In [42], the authors have shown that the finite-time synchronization of fractional-order system is shorter than the finite-time synchronization of integer-order systems. This implies that the finite-time of synchronization for integerorder systems is also finite-time of synchronization for the fractional-order version of the same systems with the same controller involved.…”

“…In this subsection, we propose a digital cryptography scheme based on the adaptive finite-time synchronization with parameters estimation of unidirectional coupled identical commensurate fractional-order form chaotic no equilibrium LRCLSJ models developed in the previous subsection. The technique of digital cryptography to be used in the present paper is an improved version of the method developed and implemented in [42][43][44] but we improve these methods. In [42], the authors used the adaptive finite-time synchronization with parameter estimation for message encryption; meanwhile in the present work we use the adaptive finite-time synchronization with parameters estimation which is recognized to be more robust than its counterpart [41].…”

“…The technique of digital cryptography to be used in the present paper is an improved version of the method developed and implemented in [42][43][44] but we improve these methods. In [42], the authors used the adaptive finite-time synchronization with parameter estimation for message encryption; meanwhile in the present work we use the adaptive finite-time synchronization with parameters estimation which is recognized to be more robust than its counterpart [41]. Cryptography is a way to encode a message by changing its original message form into another different message whose conversion rule is known only by the sender.…”

Robust finite-time synchronization of uncertain chaotic systems: application on Duffing-Holmes system and chaos gyros

“…A control Lyapunov function (CLF) scheme has also been reported for finite-time synchronization of chaotic systems (Wang, Han, Xie, & Zhang, 2009;Yu, 2010). The synchronization of uncertain fractional-order chaotic systems in finite-time has been studied by Li and Zhang (2016) and Kengne, Tchitnga, Mezatio, Fomethe, and Litak (2017). Abdurahman, Jiang, and Teng (2016) studied finite-time synchronization for a class of fuzzy neural networks with time-varying delays.…”