A novel fractional-order hyperchaotic system and its synchronization

In this paper,a novel hyperchaotic system with one nonlinear term and its fractional order system are proposed.Furthermore,synchronization between two fractional-order systems with different fractional-order values is achieved.The proposed synchronization scheme is simple and theoretically rigorous.Numerical simulations are in agreement with the theoretical analysis.     

A fractional order hyperchaotic system derived from a Liu system and its circuit realization

In this paper we propose a novel four-dimensional fractional order hyperchaotic system derived from a Liu system.Electronics workbench(EWB) and Matlab simulations show the dynamical behavior of the proposed four-dimensional fractional order hyperchaotic system.Finally,after separately using EWB and Matlab,an electronic circuit is designed to realize the novel four-dimensional fractional order hyperchaotic system and the experimental circuit results are obtained which are identical to software simulations.     

A fractional order hyperchaotic system derived from Liu system and its circuit realization

In this paper we propose a novel four-dimensional fractional order hyperchaotic system derived from Liu system. Electronics workbench (EWB) and Matlab simulations show the dynamical behavior of the proposed four-dimensional fractional order hyperchaotic system. Finally, after separately using EWB and Matlab, an electronic circuit is designed to realize the novel four-dimensional fractional order hyperchaotic system and the experimental circuit results are obtained which are identical to software simulations.     

Hybrid projective synchronization of chaotic fractional order systems with different dimensions

The hybrid projective synchronization of different dimensional fractional order chaotic systems is investigated in this paper. It is shown that the slave system can be synchronized with the projection of the master system generated through state transformation. Based on the stability theorem of linear fractional order systems, a suitable controller for achieving the synchronization is given. The hybrid projective synchronization between the fractional order chaotic system and hyperchaotic system is successfully achieved in both reduced order and increased order. The corresponding numerical results verify the effectiveness of the proposed method.     

Stability conditions, hyperchaos and control in a novel fractional order hyperchaotic system

The stability conditions in fractional order hyperchaotic systems are derived. These conditions are applied to a novel fractional order hyperchaotic system. The proposed system is also shown to exhibit hyperchaos for orders less than 4. Based on the Routh-Hurwitz conditions, the conditions for controlling hyperchaos via feedback control are also obtained. A specific condition for controlling only fractional order hyperchaotic systems is achieved. Numerical simulations are used to verify the theoretical analysis.     

分数阶超混沌Chen系统和分数阶超混沌Rssler系统的异结构同步

分数阶系统具有更大的密钥空间,然而异结构的分数阶系统在保密通信领域更具有普遍性,因此,研究异结构的分数阶同步问题具有重要的意义.本文讨论了分数阶超混沌Chen系统和分数阶超混沌Rossler系统的异结构同步问题,基于分数阶系统稳定性理论,应用主动控制同步法和自适应控制同步法来设计各自不同的控制器,使得响应系统和驱动系统同步.数值仿真表明了本文所研究方法的可行性和有效性.     

Synchronization of hyperchaotic Lorenz system based on passive control

Synchronization of a hyperchaotic Lorenz system is discussed using passive control. Based on the properties of a passive system, a passive controller is designed and the synchronization between two hyperchaotic Lorenz systems under different initial conditions is realized. Simulation results show the proposed synchronization method to be effective.     

分数阶超混沌Chen系统和分数阶超混沌 Rössler系统的异结构同步

分数阶系统具有更大的密钥空间, 然而异结构的分数阶系统在保密通信领域更具有普遍性, 因此, 研究异结构的分数阶同步问题具有重要的意义. 本文讨论了分数阶超混沌Chen系统和分数阶超混沌Rössler系统的异结构同步问题, 基于分数阶系统稳定性理论, 应用主动控制同步法和自适应控制同步法来设计各自不同的控制器, 使得响应系统和驱动系统同步. 数值仿真表明了本文所研究方法的可行性和有效性.     

基于分数阶滑模面控制的分数阶超混沌系统的投影同步

本文通过设计一个新型的含分数阶滑模面的滑模控制器,应用主动控制原理和滑模控制原理,实现了一个新分数阶超混沌系统和分数阶超混沌Chen系统的投影同步.应用Lyapunov理论,分数阶系统稳定理论和分数阶非线性系统性质定理对该控制器的存在性和稳定性分别进行了分析,并得到了异结构分数阶超混沌系统达到投影同步的稳定性判据.数值仿真采用分数阶超混沌Chen 系统和一个新分数阶超混沌系统的投影同步,仿真结果验证了方法的有效性. 关键词： 分数阶滑模面滑模控制器 稳定性分析 分数阶超混沌系统 投影同步     

Bidirectional Partial Generalized Synchronization in Chaotic and Hyperchaotic Systems via a New Scheme

In this paper, a bidirectional partial generalized (lag, complete, and anticipated) synchronization of a class of continuous-time systems is defined. Then based on the active control idea, a new systematic and concrete scheme is developed to achieve bidirectional partial generalized (lag, complete, and anticipated) synchronization between two chaotic systems or between chaotic and hyperchaotic systems. With the help of symbolic-numerical computation, we choose the modified Chua system, Lorenz system, and the hyperchaotic Tamasevicius-Namajunas-Cenys system to illustrate the proposed scheme. Numerical simulations are used to verify the effectiveness of the proposed scheme. It is interesting that partial chaos synchronization not only can take place between two chaotic systems, but also can take place between chaotic and hyperchaotic systems. The proposed scheme can also be extended to research bidirectional partial generalized (lag, complete, and anticipated) synchronization between other dynamical systems.     

基于非线性控制的超混沌Chen系统混沌同步

研究了基于非线性控制的超混沌Chen系统的混沌同步问题.基于Lyapunov稳定性理论，设计了非线性控制器，改进了Jiang和Huang等设计的同步误差系统的Lyapunov函数形式，理论证明了超混沌Chen系统的自同步和超混沌Chen系统与超混沌R?ssler系统的异结构同步.数值模拟进一步验证了所提出方案的有效性. 关键词： 超混沌Chen系统 自同步 异结构同步 非线性控制器     

Modified adaptive controller for synchronization of incommensurate fractional-order chaotic systems

We investigate the synchronization of a class of incommensurate fractional-order chaotic systems,and propose a modified adaptive controller for fractional-order chaos synchronization based on the Lyapunov stability theory,the fractional order differential inequality,and the adaptive strategy.This synchronization approach is simple,universal,and theoretically rigorous.It enables the synchronization of0 fractional-order chaotic systems to be achieved in a systematic way.The simulation results for the fractional-order Qi chaotic system and the four-wing hyperchaotic system are provided to illustrate the effectiveness of the proposed scheme.     

Chaos synchronization between two different 4D hyperchaotic Chen systems

This paper presents chaos synchronization between two different four-dimensional (4D) hyperchaotic Chen systems by nonlinear feedback control laws. A modified 4D hyperchaotic Chen system is obtained by changing the nonlinear function of the 4D hyperchaotic Chen system, furthermore, an electronic circuit to realize two different 4D hyperchaotic Chen systems is designed. With nonlinear feedback control method, chaos synchronization between two different 4D hyperchaotic Chen systems is achieved. Based on the stability theory, the functions of the nonlinear feedback control for synchronization of two different 4D hyperchaotic Chen systems is derived, the range of feedback gains is determined. Numerical simulations are shown to verify the theoretical results.     

The synchronization method for fractional-order hyperchaotic systems

In this paper, a function cascade synchronization method for fractional-order hyperchaotic systems is introduced to achieve the synchronization of two identical fractional-order hyperchaotic systems. It is shown that the method is not only theoretically rigorous, practically feasible, but also a more general one, which contains the complete synchronization, modified projective synchronization and anti-phase synchronization. In order to valid the effectiveness of the proposed method, we give two illustrative examples. Suitable controllers are designed and the function cascade synchronization for fractional-order hyperchaotic systems is achieved. Numerical simulations are performed and shown to fit with our analysis results.     

Adaptive synchronization of hyperchaotic systems via passivity feedback control with time-varying gains

A passivity feedback control scheme with time-varying gains is proposed for adaptive synchronization of hyperchaotic systems. By transforming the synchronization error dynamics into an equivalent passive system, a synchronization control law with time-varying gains is achieved and the convergence of the synchronization errors is guaranteed. The feasibility and effectiveness of the proposed scheme is demonstrated through its application to hyperchaotic Lü systems.     

Lag projective synchronization in fractional-order chaotic (hyperchaotic) systems

In this Letter, a new lag projective synchronization for fractional-order chaotic (hyperchaotic) systems is proposed, which includes complete synchronization, anti-synchronization, lag synchronization, generalized projective synchronization. It is shown that the slave system synchronizes the past state of the driver up to a scaling factor. A suitable controller for achieving the lag projective synchronization is designed based on the stability theory of linear fractional-order systems and the pole placement technique. Two examples are given to illustrate effectiveness of the scheme, in which the lag projective synchronizations between fractional-order chaotic Rössler system and fractional-order chaotic Lü system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved. Corresponding numerical simulations are also given to verify the analytical results.     

Modified function projective combination synchronization of hyperchaotic systems

In this work, a novel combination synchronization scheme in which synchronization of a new combination hyperchaotic drive system formed by combining state variables of the original drive system with appropriate scaling factors with a response hyperchaotic system is considered. A self-combination system is constructed from hyperchaotic Lorenz system by combining state variables of the Lorenz system with appropriate scaling factors. Modified function projective synchronization between the newly constructed combination hyperchaotic Lorenz system and hyperchaotic Lu system is investigated using adaptive method. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two systems as modified function projective synchronized. Numerical simulations are done to show the validity and effectiveness of the proposed synchronization scheme.     

Generalized projective synchronization of a class of chaotic (hyperchaotic) systems with uncertain parameters

In this paper is investigated the generalized projective synchronization of a class of chaotic (or hyperchaotic) systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic (hyperchaotic) systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic Lü system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.     

Adaptive synchronization of hyperchaotic Lü system with uncertainty

This paper presents a novel adaptive control scheme for synchronization of the latest hyperchaotic Lü system. Based on the Lyapunov stability theory, a feedback controller and a parameter update law are designed for the synchronization of hyperchaotic L\"{u} systems with uncertainty. Numerical simulations are given to demonstrate the validity of the synchronization technique.     

Adaptive synchronization of a hyperchaotic L system based on extended passive control

This paper investigates the adaptive synchronization of hyperchaotic Lü systems based on the method of extended passive control. By combining the feedback control, the extended passive control method with two output variables is developed, which can synchronize hyperchaotic Lü systems asymptotically and globally more easily without knowing the bound of state of the hyperchaotic system. Adaptive laws are introduced to estimate the unknown parameters as well. Simulation results show the effectiveness and flexibility of the proposed control scheme.