Synchronisation and Circuit Model of Fractional-Order Chaotic Systems with Time-Delay

Design of a new voice cryptosystem based on the global Mittag-Leffler synchronization of mismatched chaotic systems with unknown parameters, fractional orders, time delays and external disturbances

“…Although [14] has used smaller control inputs than [13], it has ignored the effect of time delay on the systems dynamics. While, because of the limited speed of data processing, there is always a time delay in practical systems [15]. On the other hand, [13] and [14] have used chaotic systems with identical fractional orders to design their voice cryptosystems.…”

Convergence criteria for nonhomogeneous linear nonautonomous real‐order time‐delay systems

“…Recently, the analysis and control design of various systems that involve time delays have received significant attention from various researchers in modern fractional engineering control practice. [15][16][17][18][19][20][21][22] For instance, Deng et al 15 showed that it is possible to synchronize the states of fractional time-delayed Duffing systems by the utilization of linear stability theory. Using the time-delayed feedback control, Gjurchinovski et al 16 showed that it is possible to stabilize the states and unstable periodic orbits in fractional-order chaotic systems.…”

“…Moreover, many control techniques such as linear feedback control and delayed feedback control have been proposed for controlling and synchronizing the unsteady dynamics of real-order time-delay systems. [18][19][20][21][22] We are often interested in the asymptotic convergence of nonautonomous real-order systems that involve delay or no delay because it provides sufficient information to analyze the response of the system. Thus, it enables one to effectively control the unsteady-steady dynamics by using the appropriate control input functions.…”

“…Recently, the analysis and control design of various systems that involve time delays have received significant attention from various researchers in modern fractional engineering control practice 15–22 . For instance, Deng et al 15 showed that it is possible to synchronize the states of fractional time‐delayed Duffing systems by the utilization of linear stability theory.…”

“…Wang et al 17 investigated the nonlinear dynamics financial system with the effect of delay in some variables of such a system. Moreover, many control techniques such as linear feedback control and delayed feedback control have been proposed for controlling and synchronizing the unsteady dynamics of real‐order time‐delay systems 18–22 …”