Hyperchaotic Liu System Research Articles

Adaptive synchronization of chaotic systems with less measurement and actuation* *Project supported by the National Natural Science Foundation of China (Grant Nos. 61573192 and 51875293).

We investigate the synchronization problem between identical chaotic systems only when necessary measurement (output) and actuation (input) are needed to be implemented by the adaptive controllers. A sufficient condition is derived based on the Lyapunov stability theory and Schur complementary lemma. Moreover, the theoretic result is applied to the Rikitake system and the hyperchaotic Liu system to show its effectiveness and correctness. Numerical simulations are presented to verify the results.

Delayed outputs fractional-order hyperchaotic systems synchronization for images encryption

Communication networks, play a major role in keeping us connected and sharing the details of our lives with each other. The main driver of multimedia data transmission is to enhance security protection of this multimedia data (speech, image and video). In this paper we addresses the synchronization problem of the masterslave type via a static error feedback. Sufficient conditions expressed by means of linear matrix inequalities (LMI) for the synchronization of fractional-order hyperchaotic systems with a known time delay between them is presented. The delay-dependent criterion is given based upon a Lyapunov function. We take the fractional-order hyperchaotic Liu system as an illustrative example to demonstrate the effectiveness of the proposed synchronization scheme. Moreover, as an application an images cryptosystem is presented. We considered two scenarios corresponding to the transmission channel, under occlusion attack and under noisse addition respectively. Results for the studied scenarios are presented and compared. The extensive simulation results prove that proposed cryptosystem has clear advantage over other proposed in the litterature.

Difference Synchronization of Identical and Nonidentical Chaotic and Hyperchaotic Systems of Different Orders Using Active Backstepping Design

This paper introduces a new type of synchronization scheme, referred to as difference synchronization scheme, wherein the difference between the state variables of two master [slave] systems synchronizes with the state variable of a single slave [master] system. Using the Lyapunov stability theory and the active backstepping technique, controllers are derived to achieve the difference synchronization of three identical hyperchaotic Liu systems evolving from different initial conditions, as well as the difference synchronization of three nonidentical systems of different orders, comprising the 3D Lorenz chaotic system, 3D Chen chaotic system, and the 4D hyperchaotic Liu system. Numerical simulations are presented to demonstrate the validity and feasibility of the theoretical analysis. The development of difference synchronization scheme has increases the number of existing chaos synchronization scheme.

Hybrid chaos synchronization between two different hyperchaotic systems via two approaches

This paper deals with the hybrid synchronization between two non-identical 4D hyperchaotic systems; Modified hyperchaotic Pan system and hyperchaotic Liu system via nonlinear control technique, based on two analytical approaches; Lyapunov’s second method and Gardano’s method. We compare between the two approaches and notice the Lyapunov stability theory is need to modify a quadratic Lyapunov function at some time, and furthermore, it’s failing in other cases. For this reason, this Letter is using a new analytical approach which doesn’t need any modified, what distinguishes this method and makes it better than the Lyapunov approach. Theoretical and numerical simulations are given to illustrate and verify the results.

Three Important Phenomena of Chaos Synchronization Between Two Different Hyperchaotic Systems via Adaptive Control Method

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.

Image Encryption Based on Hyperchaotic Liu system Algorithm

Image Encryption Based on Hyperchaotic Liu system Algorithm

Adaptive Chaos Control And Synchronization of Hyperchaotic LIU System

The hyperchaotic Liu system (Wang and Liu, 2006) is one of the important models of four-dimensional hyperchaotic systems. This paper investigates the adaptive chaos control and synchronization of hyperchaotic Liu system with unknown parameters. First, adaptive control laws are designed to stabilize the hyperchaotic Liu system to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos synchronization of identical hyperchaotic Liu systems with unknown parameters. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive chaos control and synchronization schemes.

Hybrid Chaos Synchronization of Hyperchaotic LIU And Hyperchaotic CHEN Systems by Active Nonlinear Control

This paper investigates the hybrid chaos synchronization of identical 4-D hyperchaotic Liu systems (2006), 4-D identical hyperchaotic Chen systems (2005) and hybrid synchronization of 4-D hyperchaotic Liu and hyperchaotic Chen systems. The hyperchaotic Liu system (Wang and Liu, 2005) and hyperchaotic Chen system (Li, Tang and Chen, 2006) are important models of new hyperchaotic systems. Hybrid synchronization of the 4-dimensional hyperchaotic systems addressed in this paper is achieved through complete synchronization of two pairs of states and anti-synchronization of the other two pairs of states of the underlying systems. Active nonlinear control is the method used for the hybrid synchronization of identical and different hyperchaotic Liu and hyperchaotic Chen and the stability results have been established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the proposed nonlinear control method is effective and convenient to achieve hybrid synchronization of the hyperchaotic Liu and hyperchaotic Chen systems. Numerical simulations are shown to demonstrate the effectiveness of the proposed chaos synchronization schemes.

A NOVEL FRACTIONAL-ORDER HYPERCHAOTIC SYSTEM AND ITS CIRCUIT REALIZATION

In this paper, a fractional-order hyperchaotic system evolved from Liu system is proposed. Based on the theory of fractional calculus, a novel circuit diagram is designed for hardware implementation of the fractional-order hyperchaotic Liu system. Furthermore, implementation results reveal that hyperchaos can be generated in the hyperchaotic Liu system with the system order as low as 3.6 and numerical analysis results demonstrate that the lowest order of the fractional-order Liu system is 0.4.

Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques

In this paper, recursive and active backstepping nonlinear techniques are employed to design control functions for the respective, control, and synchronization of the new hyperchaotic Liu system. The designed recursive backstepping nonlinear controllers are capable of stabilizing the hyperchaotic Liu system at any position as well as controlling it to track any trajectory that is a smooth function of time. The designed active backstepping nonlinear controllers are effective in globally synchronizing two identical hyperchaotic Liu systems evolving from different initial conditions. The results are all validated by numerical simulations.

Circuitry implementation of a novel nonautonomous hyperchaotic Liu system based on sine input

Based on the three-dimensional Liu system with a nonlinear term of square, this paper appends a state variable to the system, and further adds a driving signal of the sine signal to construct a novel 4-demensional nonautonomous hyperchaotic Liu system. The appended variable is formed by the product of the nonlinear quadratic term of the original state variables and the driving signal. Through adjusting the frequency of the driving signal, the system can be controlled to show some different dynamic behaviors. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the novel systems are analyzed. Furthermore, the corresponding hardware circuits are implemented. Both the experimental results and the simulation results confirm that the method is feasible. The method, which adjusts the frequency of the input sine signal to control the system to show different dynamic behaviors, can make the dynamic property of the system become more complex, but easier to be controlled accurately as well.

Circuitry implementation of a novel four-dimensional nonautonomous hyperchaotic Liu system and its experimental studies on synchronization control

Based on the three-dimensional Liu chaotic system, this paper appends a feedback variable to construct a novel hyperchaotic Liu system. Then, a control signal is further added to construct a novel nonautonomous hyperchaotic Liu system. Through adjusting the frequency of the control signal, the chaotic property of the system can be controlled to show some different dynamic behaviors such as periodic, quasi-periodic, chaotic and hyperchaotic dynamic behaviours. By numerical simulations, the Lyapunov exponent spectrums, bifurcation diagrams and phase diagrams of the two new systems are studied, respectively. Furthermore, the synchronizing circuits of the nonautonomous hyperchaotic Liu system are designed via the synchronization control method of single variable coupling feedback. Finally, the hardware circuits are implemented, and the corresponding waves of chaos are observed by an oscillograph.