Fractional calculus in discrete-time systems is a recent research topic. The fractional maps introduced in the literature often display chaotic attractors belonging to the class of “self-excited attractors”. The field of fractional map with “hidden attractors” is completely unexplored. Based on these considerations, this paper presents the first example of fractional map without equilibria showing a number of hidden attractors for different values of the fractional order. The presence of the chaotic hidden attractors is validated via the computation of bifurcation diagrams, maximum Lyapunov exponent, 0–1 test, phase diagrams, complexity, and entropy. Finally, an active controller with the aim for stabilizing the proposed fractional map is successfully designed.

By converting the resistive capacitive shunted junction model to a jerk oscillator, an autonomous chaotic Josephson jerk oscillator which can belong to oscillators with hidden and self-excited attractors is designed. The proposed autonomous Josephson jerk oscillator has two or no equilibrium points depending on DC bias current. The stability analysis of the two equilibrium points shows that one of the equilibrium points is unstable while for the other equilibrium point, the existence of a Hopf bifurcation is established. The dynamical behavior of autonomous Josephson jerk oscillator is analyzed by using standard tools of nonlinear analysis. For a suitable choice of the parameters, an autonomous Josephson jerk oscillator can generate antimonotonicity, periodic oscillations, self-excited chaotic attractors, hidden chaotic attractors, hidden chaotic bubble attractors, and coexistence between periodic and chaotic self-excited attractors. Finally, a text cryptographic encryption scheme with the help of generalized function projective synchronization of the proposed autonomous Josephson jerk oscillators in hidden chaotic attractor regime is illustrated through a numerical example, showing that a high-level security device can be produced using this system.

The multi-area multi-source power system (MAMSPS), which uses a variety of power sources including gas, hydro, thermal, and renewable energy, has recently been implemented to balance the growing demand for electricity and the overall capacity for power generation. In this paper, an integral sliding mode control with a single-phase technique (ISMCSP) is applied to two areas, with each area including gas–wind–thermal power systems with HVDC system. Firstly, a two-area gas–wind–thermal power system with HVDC (TAGWTPSH) is the first model in this scheme to consider the parameter uncertainties of a MAMSPS. Secondly, sliding mode design law with a single-phase technique is introduced to alleviate chattering and oscillation problems. Then, power system stability is ensured by the Lyapunov control theory based on the new LMIs technique. Thirdly, the ISMCSP’s effectiveness in a MAMSPS is also assessed under random load patterns and parameter variations regarding settling time and over-/undershoot. The ISMCSP was created to alter the fundamental sliding mode control, and therefore the suggested approach performs better than recently published approaches. This is demonstrated by the frequency overshoot deviation value in frequency deviations: 0.7 × 10⁻³ to 2.8 × 10⁻³ for the TAGWTPSH with the suggested ISMCSP. In the last case, for random changes in load from −0.4 to +0.5 p. u, the proposed ISMCSP method still stabilizes the frequency of the areas meeting the standard requirements for AGC.

The paper deals with modification of super-twisting algorithm in sliding mode speed controller for predictive control of induction motor. At very-low-speed and/or high-load torque regions, the conventional proportional-integral controller gives poor speed response performance. In order to enhance the performance, sliding mode control (SMC) is deployed. However, the conventional SMC often owns high-chattering control signal. Super-twisting algorithm is utilized to reduce the chattering. In order to obtain high accuracy of the speed response, boundaries of the disturbance term and its time derivative are defined using dynamic equation of the motor. Simulations with the predict control of three controllers confirm the superior performance of the proposed super-twisting algorithm in terms of normalized integral time absolute error and relative final error of the motor speed.