Nonsingular Integral-Type Dynamic Finite-Time Synchronization for Hyper-Chaotic Systems

Abstract

In this study, the synchronization problem of chaotic systems using integral-type sliding mode control for a category of hyper-chaotic systems is considered. The proposed control method can be used for an extensive range of identical/non-identical master-slave structures. Then, an integral-type dynamic sliding mode control scheme is planned to synchronize the hyper-chaotic systems. Using the Lyapunov stability theorem, the recommended control procedure guarantees that the master-slave hyper-chaotic systems are synchronized in the existence of uncertainty as quickly as possible. Next, in order to prove the new proposed controller, the master-slave synchronization goal is addressed by using a new six-dimensional hyper-chaotic system. It is exposed that the synchronization errors are completely compensated for by the new control scheme which has a better response compared to a similar controller. The analog electronic circuit of the new hyper-chaotic system using MultiSIM is provided. Finally, all simulation results are provided using MATLAB/Simulink software to confirm the success of the planned control method.

Adomian Decomposition, Dynamic Analysis and Circuit Implementation of a 5D Fractional-Order Hyperchaotic System

“…For the design of fractional-order chaotic circuits, most of the circuits are designed with the order of 0.1~0.9. In this paper, the maximum frequency of the system is 100 Hz, and the error is 2 dB by using the method of reference [30,31]. The expansion formula of fractional order q (0.90~0.99) of the system is calculated as shown in Table 1.…”

“…Chaotic system (6) is realized by the modular circuits of resistors with different resistance values, capacitors with different capacitance values, operational amplifier LM741 and multipliers AD633 and 1/s 0.96 . The working voltage of operational amplifier LM741 and multiplier AD633 is limited, so the system linearity is reduced to 0.1 times the original circuit design [31].…”

“…The results are displayed in real-time on the oscilloscope, as shown in Figure 10. AD633 is limited, so the system linearity is reduced to 0.1 times the original circuit design [31]. Multisim13 is used to simulate the designed analog circuit, and the horizontal axis is adjusted during the simulation process.…”

A new 10-D hyperchaotic system with coexisting attractors and high fractal dimension: Its dynamical analysis, synchronization and circuit design

“…Singh et al [ 8 ] proposed of the 5-D hyperchaotic system with stable equilibrium point and the proposed system exhibits multistability and transient chaotic behavior. Alattas et al [ 9 ] proposed of the synchronization problem of hyperchaotic systems using integral-type sliding mode control for the 6-D hyperchaotic systems and presented of the analog electronic circuit using MultiSIM. Lagmiri et al [ 10 ] constructed of the two new 7D hyperchaotic systems and to investigate the dynamics and synchronization of these new systems using the theory of observers.…”

Dynamical System in Chaotic Neurons with Time Delay Self-Feedback and Its Application in Color Image Encryption

“…e study of the chaotic system has attracted the attention of scholars. In [16], the synchronization problem of chaotic systems using integral-type sliding mode control for a category of hyperchaotic systems is considered, controlling the nonlinear systems and chaotic behaviors for achievement of finite-time synchronization. In [17], an adaptive nonsingular terminal sliding mode control method based on obstacle function is proposed to solve the problem of robust stability of disturbed nonlinear systems.…”