Modified Projective Synchronization of Chaotic Systems with Noise Disturbance, an Active Nonlinear Control Method

The synchronization problem of chaotic systems using active modified projective nonlinear control method is rarely addressed. Thus the concentration of this study is to derive a modified projective controller to synchronize the two chaotic systems. Since, the parameter of the master and follower systems are considered known, so active methods are employed instead of adaptive methods. The validity of the proposed controller is studied by means of the Lyapunov stability theorem. Furthermore, some numerical simulations are shown to verify the validity of the theoretical discussions. The results demonstrate the effectiveness of the proposed method in both speed and accuracy points of views

Robust adaptive anti-synchronization control of multiple uncertain chaotic systems of different orders

The precise anti-synchronization control of uncertain chaotic systems has always remained an interesting problem. The anti-synchronization control of multiple different orders uncertain chaotic systems increases the complexity and enhances the security of the information signal in secure communications. Hence, it confines the hacking in digital communication systems. This paper proposes a novel adaptive control technique and studies the double combination anti-synchronization of multiple different orders uncertain chaotic systems. The proposed adaptive feedback control technique consists of three fundamental nonlinear components. Each component accomplishes a different objective; (i) stability of the closed-loop, (ii) smooth and fast convergence behaviour of the anti-synchronization error, and (iii) disturbance rejection. The theoretical analysis in (i) to (iii) uses the Lyapunov stability theory. This paper also provides parameters adaptation laws that stabilize the uncertain parameters to some constants. The paper discusses the simulation results of two representative examples of four different orders uncertain chaotic systems. These examples demonstrate anti-synchronization among hyperchaotic Lü, uncertain chaotic Shimizu Morioka, uncertain second-order nonlinear duffing, and uncertain parametrically excited second-order nonlinear pendulum systems. The computer-based simulation results certify the efficiency and performance of the proposed anti-synchronization control approach and compare them with peer works

A novel 4 dimensional hyperchaotic system with its control, Synchronization and Implementation

This paper presents a new hyperchaotic system which shows some interesting features, the system is 4-dimensional with 4 nonlinearities. An extensive numerical analysis has showed that the system has some interesting features and strange behaviors. The numerical analysis includes studying the effect of system parameters and initial conditions. Some of the important properties of the system with parameter set, in which the system is hyperchaotic, such as Lyapunov exponents and Lyapunov dimension, dissipation and symmetry are found and discussed. In the next part of our work, a tracking controller for the proposed system is designed and then a synchronization control system for two identical systems is designed. The design procedure uses combination of a simple synergetic control with adaptive updating laws to identify the unknown parameters derived basing on Lyapunov theorem. Hardware implementation based on microcontroller unit (MCU) board is proposed and tested and used to experimentally validate the designed control and synchronization systems. As an application, the designed synchronization system is used as a secure analogue communication system. Using MATLAB, Simulation study for the control and synchronization systems is presented. The simulation and experimental study have been showed excellent results

Dynamic system with no equilibrium and its chaos anti-synchronization

Recently, systems with chaos and the absence of equilibria have received a great deal of attention. In our work, a simple five-term system and its anti-synchronization are presented. It is special that the system has a hyperbolic sine nonlinearity and no equilibrium. Such a system generates chaotic behaviours, which are verified by phase portraits, positive Lyapunov exponent as well as an electronic circuit. Moreover, the system displays multistable characteristic when changing its initial conditions. By constructing an adaptive control, chaos anti-synchronization of the system with no equilibrium is obtained and illustrated via a numerical example

An optimal control for complete synchronization of 4D Rabinovich hyperchaotic systems

This paper derives new results for the complete synchronization of 4D identical Rabinovich hyperchaotic systems by using two strategies: active and nonlinear control. Nonlinear control strategy is considered as one of the powerful tool for controlling the dynamical systems. The stabilization results of error dynamics systems are established based on Lyapunov second method. Control is designed via the relevant variables of drive and response systems. In comparison with previous strategies, the current controller (nonlinear control) focuses on convergence speed and the minimum limits of relevant variables. Better performance is to achieve full synchronization by designing the control with fewer terms. The proposed control has certain significance for reducing the time and complexity for strategy implementation

A new 4-D hyperchaotic hidden attractor system: Its dynamics, coexisting attractors, synchronization and microcontroller implementation

In this paper, a simple 4-dimensional hyperchaotic system is introduced. The proposed system has no equilibria points, so it admits hidden attractor which is an interesting feature of chaotic systems. Another interesting feature of the proposed system is the coexisting of attractors where it shows periodic and chaotic coexisting attractors. After introducing the system, the system is analyzed dynamically using numerical and theoretical techniques. In this analysis, Lyapunov exponents and bifurcation diagrams have been used to investigate chaotic and hyperchaotic nature, the ranges of system parameters for different behaviors and the route for chaos and coexisting attractors regions. In the next part of our work, a synchronization control system for two identical systems is designed. The design procedure uses a combination of simple synergetic control with adaptive updating laws to identify the unknown parameters derived basing on Lyapunov theorem. Microcontroller (MCU) based hardware implementation system is proposed and tested by using MATLAB as a display side. As an application, the designed synchronization system is used as a secure analog communication system. The designed MCU system with MATLAB Simulation is used to validate the designed synchronization and secure communication systems and excellent results have been obtained