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The current study is concerned with the dynamical investigation, synchronization, and engineering application of a new variable-order fractional neural network. The model of the variable-order fractional neural network is presented, and its chaotic behavior is studied through well-known dynamical tools. Then, a new control technique is proposed for the control of the system. Although finite-time estimators considerably enhance the performance of controllers, studies that offer finite-time estimators for the control of fractional-order systems are rare in the literature. Motivated by this, as a novel approach, the proposed control technique is equipped with a finite-time estimator, which is able to approximate highly nonlinear disturbances and uncertainties. The stability and finite-time convergence of the sliding surface and error dynamics based on the proposed control technique are proven. Through numerical simulations, the effectiveness of the designed control scheme in the presence of complex time-varying disturbances is illustrated. Then, a voice encryption application has been implemented in order to show the feasibility of data security applications of the proposed variable-order neural network. Finally, to investigate the effectiveness of the implemented data security application, the entropy values for original, encrypted, and decrypted voice data are presented. Numerical analyses of encryption clearly confirm that encryption is done securely and there is no corruption or data loss in encryption and decryption processes. [ABSTRACT FROM AUTHOR]

Despite the existence of promising methods for controlling complex systems, there is still a need for further advancement in controlling and synchronizing fractional systems. This is even more monumental when it comes to practical applications with faults and physical constraints present in their control actuators. To address this issue, the current study proposes a new control technique that utilizes a recurrent neural network-based finite-time super-twisting algorithm for fractional-order systems. The proposed controller is enhanced with an intelligent observer to account for faults and limitations that may be present in the control actuator of the fractional-order systems. The proposed method allows the system to be regulated even in the presence of control input constraints and faults. Moreover, the proposed technique guarantees that the closed-loop system will converge in a finite amount of time. The control design is explained in detail, and its finite-time stability is proven. To evaluate the performance of the controller, we applied it to two different fractional-order systems that were subject to control input limitations and faults. The outcomes of the proposed approach were then compared with those obtained using a state-of-the-art technique for fractional-order systems to further validate the effectiveness of our proposed approach. • A controller proposed for fractional systems using recurrent neural network-based finite-time super-twisting algorithm. • Controller enhanced with intelligent observer to handle faults and limitations in control actuators. • Proposed method enables system regulation despite control input constraints and faults. • Guaranteed finite-time convergence of closed-loop system. • Performance evaluated on two fractional-order systems, outperforming state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

In the present paper, for the first time, we propose a variable-order hyperchaotic system for information security. Firstly, we study the dynamical behaviors of a memristor oscillator through well-known numerical and analytical tools, such as the Lyapunov exponents, stability of equilibria, and bifurcation diagram. Then as an engineering application, a variable-order fractional version of the system is proposed for sound encryption. In comparison with integer and conventional constant fractional-order chaotic memristor oscillator, the proposed variable-order fractional system shows more complex characteristics and more degrees of freedom due to the existence of time-varying fractional derivatives. Thus, the proposed system is an appropriate choice for data transmission and information security. To illustrate the proper performance of the suggested system for encryption purposes, sound encryption is successfully performed, and its excellent results are demonstrated. The predictor-corrector method is utilized for numerical simulation. Then, a new type-2 fuzzy disturbance observer-based robust control is offered for synchronization of the variable-order hyperchaotic system. The stability and convergence of the disturbance estimator and closed-loop system are proven. Lastly, the synchronization results, which confirm the appropriate performance of the proposed method in the presence of the external disturbances, are demonstrated. [ABSTRACT FROM AUTHOR]

• Spectral entropy and spectral Min-Entropy are computed, and the phenomenon of multi-stability is shown. • A new chattering-free robust sliding mode controller with a neural network observer is proposed. • Based on the Lyapunov stability theorem, the asymptotical stability of the closed-loop system is confirmed. • Numerical results demonstrate the chattering-free and effective performance of the proposed control method. An immense body of research has focused on chaotic systems, mainly because of their interesting applications in a wide variety of fields. A comprehensive understanding and synchronization of chaotic systems play pivotal roles in practical applications. To this end, the present study investigates a multi-stable fractional-order chaotic system. Firstly, some dynamical features of the system are described, and the chaotic behaviour of the system is verified. Then, both spectral entropy and spectral Min-Entropy are computed, and the phenomenon of multi-stability is shown. Besides, the combination of a new chattering-free robust sliding mode controller with a neural network observer is proposed for the synchronization of the fractional-order system. With the neural network estimator, unknown functions of the system are obtained, and the effects of disturbances are completely taken into account. Also, based on the Lyapunov stability theorem, the asymptotical stability of the closed-loop system is confirmed. Lastly, the proposed control technique is applied to the fractional-order system. Numerical results demonstrate the chattering-free and effective performance of the proposed control method for uncertain systems in the presence of unknown time-varying external disturbances. [ABSTRACT FROM AUTHOR]

• The discrete-time mathematical model of the macroeconomic system is presented. • The system is studied through topological classification, bifurcation analysis, Lyapunov exponents, and manifold theory. • A fuzzy based-activation feedback controller is proposed for the synchronization of the system. Economic systems, due to their substantial effects on any society, are interesting research subject for a large family of researchers. Despite all attempts to study economic and financial systems, studies on discrete-time macroeconomic systems are rare. Hence, in the current study, we aim to investigate dynamical behavior and synchronization of these systems. At first, the discrete-time mathematical model of the macroeconomic system is presented. Then, the system is studied through topological classification, bifurcation analysis, Lyapunov exponents, and manifold theory, which are powerful tools in the investigation of nonlinear systems. This way, the features of the system are disclosed, and the existence of chaos in the system is shown. For the adequate performance of the economy, the economic systems are desired to operate in a unified manner. To this end, in the present research, a fuzzy based-activation feedback controller is proposed for the synchronization of the system. To enhance the celerity and accuracy of the proposed control for synchronization purposes, it is equipped with a fuzzy logic engine. Finally, the numerical simulations of the synchronization are presented and compared with those of a conventional activation feedback control. Numerical results verify that the proposed control technique can successfully push the states of the response system to the desired value. [ABSTRACT FROM AUTHOR]

Having found hidden hyperchaos in a 5D self-exciting homopolar disc dynamo, we study the existence of a Hopf bifurcation, which leads to unstable limit cycles bifurcating from a stable equilibrium. Hidden chaos with only stable equilibria can be observed from the Hopf bifurcation: a typical way to enable hidden attractors to be located. We then provide a new fuzzy controller, and a fast fuzzy disturbance observer, based on terminal sliding mode control for synchronization of the hyperchaotic system. Fuzzy inference is considered to weaken the chattering phenomena. Using Lyapunov stability theory, the stability of the closed-loop system is proved. Finally, simulations of synchronization are illustrated to show the efficient performance of the designed control method via external disturbances and dynamic uncertainties. [ABSTRACT FROM AUTHOR]

In today's sophisticated world, where financial systems play an increasingly important role, the application of controllers through management strategies is of crucial importance, given their vital role. An analysis of the synchronization of economic systems can provide a valuable insight into the financial synchronous development of different countries or regions around the world. In this paper, an adaptive fixed-time control strategy is presented for the function projective synchronization of drive-response hyperchaotic economic systems with unknown parameters and external perturbations. The developed controller is constructed by combining the fixed-time control approach and parametric adaptation technique. Specifically, the adaptive adjusting mechanisms are designed to estimate the unknown parameters and external perturbations, respectively. Stability investigation shows that the function projective synchronization errors under the developed controller can stabilize to the minor fields about zero in fixed time. A key feature of the developed controller is its high insensitive to unknown parameters and strong robustness against external perturbations. Finally, the effectiveness and merits of the presented control strategy are examined by simulation scenarios. • Introducing a novel adjustable fixed-time control strategy • Development of a robust controller by combining a fixed-time control approach with a parametric adaptation technique • Design of an adaptive adjusting mechanism to robust estimation of unknown time-varying parameters and external perturbations [ABSTRACT FROM AUTHOR]

In this article, a fixed-time neural control methodology is presented for the output-constrained synchronization of second-order chaotic systems with unknown parameters and perturbations. The presented controller is synthesized under the fixed-time backstepping control framework. In the virtual control law design, the barrier Lyapunov function (BLF) is introduced to tackle the output constraints. In the actual control law design, the neural network (NN) is embedded to identify the total unknown item. Stability argument shows that the resultant closed-loop system is practically fixed-time stable. A distinctive feature of the presented controller is that it is capable of stabilizing the synchronization errors in fixed time while ensuring the output constraints can always be satisfied simultaneously. The efficiency and superiority of the presented control methodology are examined through two simulated examples. • A fixed-time neural control methodology • Output-constrained synchronization of second-order chaotic systems • Fixed-time backstepping control framework [ABSTRACT FROM AUTHOR]

It is well known that the satellite attitude motion exhibits the chaotic phenomenon. This article addresses the challenging problem of chaotic attitude synchronization and anti-synchronization for master-slave satellites under unknown moments of inertia and disturbance torques. First, a fixed-time adaptive synchronization controller is designed by combining the fixed-time control technique and adaptive control technique. The parametric adaptation laws are adopted to identify the unknown parameters in the synchronization error system. Benefiting from the adaptive identifications, the proposed controller is highly robust to unknown moments of inertia and disturbance torques. The practical fixed-time stability of the resulting closed-loop system is strictly achieved. The proposed controller can guarantee all error variables in the closed-loop system regulate to the small residual sets around zero in fixed time. Then, a fixed-time adaptive anti-synchronization controller is developed in a similar way. Finally, simulations studies are conducted to demonstrate the effectiveness and excellent control performance of the proposed controllers. [ABSTRACT FROM AUTHOR]

• A new type-2 fuzzy disturbance-observer-based active control. • Robustness against unknown time-varying uncertainties and disturbances. • Investigation of the chaotic behavior of a fractional-order time-delayed system. • Synchronization of a fractional-order time-delayed financial system. In the present article, as a new approach, a fuzzy disturbance observer is combined with an active controller for the synchronization of fractional-order time-delayed systems. Since the type-2 fuzzy logic system shows better performances than the type-1 fuzzy logic system on handling the uncertainties and disturbances, the type-2 fuzzy disturbance observer is utilized in this study. The stability of the proposed method is performed using the Lyapunov stability theorem and active control concept. Then, a fractional-order time-delayed financial system has been investigated, and some features of this chaotic system have been studied. Finally, by applying the proposed control scheme, synchronization results of the fractional-order time-delayed financial system when there exist time-varying disturbances are presented. Numerical simulations demonstrate the robustness and effectiveness of the proposed control technique. [ABSTRACT FROM AUTHOR]