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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]

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]