bashir naderi

‎In this article‎, ‎we analyze a four-dimensional chaotic system‎, ‎focusing on bifurcation and the Lyapunov exponent as key characteristics under new parameter settings‎. ‎Our main goal is to control the system using a graphical algorithm based on contraction method in dynamical systems‎. ‎The controller designed using this method is simpler than most controllers for chaotic systems‎. ‎Since chaotic systems are sensitive to initial conditions‎, ‎their synchronization and control are essential challenges‎. ‎The graphic algorithm is used for both controlling and synchronizing the chaotic memristor system‎. ‎Also‎, ‎we utilize the synchronization results for secure communication‎, ‎employing master and slave systems as encryption and decryption keys‎. ‎The effectiveness of the proposed method is demonstrated through numerical simulations‎.

In this paper‎, ‎we use a graphical algorithm to control and synchronization of a chaotic system‎. ‎Most of the controllers designed for synchronizing chaotic systems are complex‎, ‎but the controllers designed using contraction and graphical methods are often simple and linear‎. ‎Therefore‎, ‎we explain the relationship between contraction analysis and the graphical method for controlling and synchronizing chaotic systems‎. ‎We apply this approach to control and synchronize the chaotic Genesio-Tesi system‎. ‎The stability of the error system in synchronization is investigated using the contraction method‎. ‎Finally‎, ‎we provide numerical simulations to demonstrate the effectiveness of the proposed method‎.

In this article, Synchronization and control methods are discussed as essential topics in science. The contraction method is an exciting method that has been studied for the synchronization of chaotic systems with known and unknown parameters. The controller and the dynamic parameter estimation are obtained using the contraction theory to prove the stability of the synchronization error and the low parameter estimation. The control scheme does not employ the Lyapunov method. For demonstrate the ability of the proposed method, we performed a numerical simulation and compared the result with the previous literature.

In this paper, a new synchronization criterion for leader-follower fractional-order chaotic systems using partial contraction theory under an undirected fixed graph is presented. Without analyzing the stability of the error system, first the condition of partial contraction theory for the synchronization of fractional systems is explained, and then the input control vector is designed to apply the condition. An important feature of this control method is the rapid convergence of all agents into a common state. Finally, numerical examples with corresponding simulations are presented to demonstrate the efficiency and performance of the stated method in controlling fractional-order systems. The simulation results show the appropriate design of the proposed control input.

This paper focuses on the anti-synchronization of two identical and non-identical chaotic fractional-order financial systems with disturbance observe (FOFSDO), such that the anti-synchronization is discussed with new parameters and disturbance in the slave system by using the nonlinear active control technique. The stability of the scheme is proved by applying the Lyapunov stability method for the error system. The result of anti-synchronization with disturbance is applied in cryptography. Numerical examples and simulation analysis indicate the application and validity of the scheme and considered system.

In this paper, a synchronization balancing control is proposed based on the contraction theory of stability for inverted pendulum. The control scheme is applied to balance an inverted pendulum mounted on a moving cart with two wheels. The equations of motion of the system are divided into two cascade systems using the control law partitioning method, which allows the designer to split the control design process into simpler parts for each isolated fragment of the main system. Then two control laws are planned for the corresponding partitions. The main aim of the closed-loop system is to balance the pendulum and synchronize the transient behavior of the system state with a reference model with time-varying parameters. The stability of method is guaranteed using the contraction theory, and the proposed control mechanism is investigated through the simulation study. The simulation result confirms the performance of the proposed controller and illustrate the feasibility of method.

In this study, the problem of consensus of multi-agent chaotic systems of fractional order is considered. Using the fractional order derivative in Caputo's sense and the classical stability theorem of linear fractional order systems as well as algebraic graph theory, sufficient conditions are provided to ensure consensus for fractional multi-agent systems. The distributed adaptive protocols of each agent are designed using local information and a detailed analysis of the leader-following consensus is presented. Some numerical simulation examples are provided to show the effectiveness of the proposed results.

In this paper, we present a new fractional-order financial system (FOFS) with the new parameters. We study the synchronization for commensurate order of the fractional-order financial system with disturbance observer (FOFSDO) on the new parameters. Also, the sensitivity analysis of the synchronization error was investigated by using the feedback control technique for the FOFSDO. The stability of the used method demonstrates by Lyapunov stability theorem. Numerical simulations are presented to ensure the validity and influence of the target feedback control design in the presence of extrinsic bounded unknown disturbance.

In this study, we propose a secure communication scheme based on the synchronization of two identical fractional-order chaotic systems. The fractional-order derivative is in Caputo sense, and for synchronization, we use a robust sliding-mode control scheme. The designed sliding surface is taken simply due to using special technic for fractional-order systems. Also, unlike most manuscripts, the fractional-order derivatives of state variables can be chosen differently. The stability of the error system is proved using the Lyapunov stability of fractional-order systems. Numerical simulations illustrate the ability and effectiveness of the proposed method. Moreover, synchronization results are applied to secure communication using the masking method. The security analysis demonstrates that the introduced algorithm has a large keyspace, high sensitivity to encryption keys, higher security, and the acceptable performance speed.

In this paper, we discuss the synchronization and anti-synchronization of two identical chaotic T-systems. The adaptive and nonlinear control schemes are used for the synchronization and anti-synchronization. The stability of these schemes is derived by Lyapunov Stability Theorem. Firstly, the synchronization and anti-synchronization are applied to systems with known parameters, then to systems in which the drive and response systems have one unknown parameter. Numerical simulations show the effectiveness and feasibility of the proposed methods.

In this paper, we introduce a new hyperchaotic complex T-system. This system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, Lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. We discuss the synchronization with certain and uncertain parameters via adaptive control. For synchronization, we use less controllers than the dimension of the proposed system. Also, we prove that the error system is asymptotically stable by using a Lyapunov function. Numerical simulations are computed to check the analytical expressions.