Synchronization of a four-wing hyperchaotic system

Pramana, 2014

This paper presents increased-order generalized synchronization (GS) of chaotic and hyperchaotic systems with different order based on active control technique. By this technique, we design suitable control functions to achieve GS between (i) a new three-dimensional (3D) chaotic system and four-dimensional (4D) hyperchaotic Lorenz system and (ii) four-dimensional hyperchaotic Lorenz system and five-dimensional (5D) hyperchaotic Lorenz system. The corresponding numerical simulation results are presented to verify the effectiveness of this technique.

TELKOMNIKA Telecommunication Computing Electronics and Control, 2020

This paper presented stability application for chaos synchronization using a 6-D hyperchaotic system of different controllers and two tools: Lyapunov stability theory and Linearization methods. Synchronization methods based on nonlinear control strategy is used. The selecting controller's methods have been modified by applying complete synchronization. The Linearization methods can achieve convergence according to the of complete synchronization. Numerical simulations are carried out by using MATLAB to validate the effectiveness of the analytical technique. 1. INTRODUCTION In recent years, the dynamical system has attracted significant attention due to its widespread applications in engineering and different scientific research as lasers, nonlinear circuits biological [1, 2], engineering [3, 4] and secure communications [5, 6]. Lorenz system is the first physical and mathematical model of a chaotic system contains real variables only which discovered in 1963 and open the way to find another chaotic system such as Chen system, Lu system, Liu system and Pan system [7-9]. Each system has a 3-D of differential equations and just one positive Lyapunov exponent [10]. One important application in the field of engineering is secure communication i.e., the messages which are made by such simple chaotic systems are not always safe [6, 11, 12]. It is suggested that this problem can be overcome by using higher-dimensional hyperchaotic systems, which have increased randomness and higher unpredictability. In 1979, Rössler discovers the first 4-D hyperchaotic system including real variables with two positive Lyapunov exponents and followed to discover another 4-D, as well as 5-D hyperchaotic with three positive Lyapunov exponents [10, 13-15] and some other systems, have been revealed. The dynamical systems with higher dimensions are effective and interesting compared with the low dimensions [16-18]. In 2015, Yang et al., proposes a 6-D hyperchaotic system including real variables and has four positive Lyapunov exponents [19]. These days, the synchronization of the mentioned systems witnessed large attention by researchers because of its important applications in the is secure communication [20-22]. Many of the papers that relate to this topic are increasing, and numerous research devoted to investigating CS of high-dimensional hyperchaotic systems based on traditional Lyapunov stability theory [23-25]. Lyapunov stability theory is

Chaos, Solitons & Fractals, 2006

This paper addresses the synchronization problem of two Lü hyperchaotic dynamical systems in the presence of unknown system parameters. Based on Lyapunov stability theory an adaptive control law is derived to make the states of two identical Lü hyperchaotic systems with unknown system parameters asymptotically synchronized. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization schemes.

Nonlinear Analysis: Modelling and Control

In this paper, we present new schemes to synchronize different dimensional chaotic and hyperchaotic systems. Based on coexistence of generalized synchronization (GS) and inverse generalized synchronization (IGS), a new type of hybrid chaos synchronization is constructed. Using Lyapunov stability theory and stability theory of linear continuous-time systems, some sufficient conditions are derived to prove the coexistence of generalized synchronization and inverse generalized synchronization between 3D master chaotic system and 4D slave hyperchaotic system. Finally, two numerical examples are illustrated with the aim to show the effectiveness of the approaches developed herein.

International Journal of Electrical and Computer Engineering (IJECE), 2021

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.

Alexandria Engineering Journal, 2018

This paper deals with the synchronization between two non-identical 4-D hyperchaotic systems. The nonlinear control technique is used for synchronization. The stability analysis of the error dynamics system is done by (i) Lyapunov's second method and (ii) Cardano's method. Four different expressions of the controller are presented in the paper and a comparison between the two methods are given. We notice that the Cardano's method is better than the Lyapunov approach. Finally, theoretical and numerical simulations are given to illustrate and verify the results.

International Journal of Theoretical and Applied Mathematics, 2017

This paper presents three important phenomena of chaos synchronization between two different hyperchaotic systems using nonlinear adaptive control strategy. In detailed, complete synchronization, anti-synchronization and hybrid synchronization with nine unknown parameters. Modified hyperchaotic Pan system is consider as drive and hyperchaotic Liu system as response system. Stabilization of error dynamics for each phenomenon is realized by satisfying Lyapunov's second method as a main tool. Theoretical analysis and numerical simulations are shown to verify the results.

TELKOMNIKA Telecommunication Computing Electronics and Control, 2020

Nonlinear control strategy was established to realize the Projective Synchronization (PS) and Hybrid Projective Synchronization (HPS) for 4-D hyperchaotic system at different scaling matrices. This strategy, which is able to achieve projective and hybrid projective synchronization by more precise and adaptable method to provide a novel control scheme. On First stage, three scaling matrices were given in order to achieving various projective synchronization phenomena. While the HPS was implemented at specific scaling matrix in the second stage. Ultimately, the precision of controllers were compared and analyzed theoretically and numerically. The long-range precision of the proposed controllers are confirmed by third stage. Keywords: Hybrid projective Hyperchaotic system Lyapunov stability Nonlinear control strategy Projective synchronization synchronization This is an open access article under the CC BY-SA license.

IFAC_ACODS-2014

In this paper hybrid synchronization between hyperchaotic and chaotic systems is presented. The hyperchaotic Lorenz-Stenflo system is used as master and the chaotic Chen system is used as slave. The global hybrid synchronization between master and slave systems is achieved by using nonlinear active control. Nonlinear controller is designed by using the relevant variables of master and slave systems. The stability of the proposed hybrid synchronization scheme is shown by using Lyapunov stability theory. MATLAB simulation is carried out to find the effectiveness of the proposed scheme. Results obtained validate the proposed theory.

2019

In this paper, we apply adaptive control method to derive new results for the global chaos synchronization of identical hyperchaotic Lorenz systems (Jia, 2007), identical hyperchaotic Lü systems (Chen, et al., 2006) and non-identical hyperchaotic Lorenz and hyperchaotic Lü systems. In this paper, we shall assume that the parameters of both master and slave systems are unknown and we devise adaptive synchronizing schemes using the estimates of parameters for both master and slave systems. Our adaptive synchronization schemes derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical hyperchaotic Lorenz and hyperchaotic Lü systems. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the uncertain hyperchaotic systems addressed in this paper.