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.     

一类四维超混沌系统的界及同步的研究

文章研究了一类四维连续自治系统,在一定条件下它只有一个平衡点,却表现出复杂的动力学行为. 文章首先分析了系统的平衡点及李雅普诺夫指数;其次对该系统的界进行了估计,给出了界的表达式.通过设计一个控制器,研究了该四维超混沌系统的完全同步,并做出了相应的数值模拟. 关键词： 超混沌系统 李雅普诺夫指数 混沌系统的界 同步     

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 new four-dimensional hyperchaotic Chen system and its generalized synchronization

Based on the Chen chaotic system, a new four-dimensional hyperchaotic Chen system is constructed, and the basic dynamic behaviours of the system were studied, and the generalized synchronization has been observed in the coupled four-dimensional hyperchaotic Chen system with unknown parameters. The Routh--Hurwitz theorem is used to derive the conditions of stability of this system. Furthermore based on Lyapunov stability theory, the control laws and adaptive laws of parameters are obtained to make generalized synchronization of the coupled new four-dimensional hyperchaotic Chen systems. Numerical simulation results are presented to illustrate the effectiveness of this method.     

Liu混沌系统的非线性反馈同步控制

研究了新型混沌系统——Liu系统的同步控制问题.基于Lyapunov稳定性理论，采用非线性反馈控制方法，给出了Liu系统实现自同步的充分条件以及控制律参数的取值范围；结合参数自适应控制方法，实现了Liu混沌系统与统一混沌系统的异结构系统快速同步.数值仿真证明了该方法的有效性. 关键词： Liu混沌系统 混沌同步 非线性反馈控制 参数自适应控制     

Projective synchronization of a hyperchaotic system via periodically intermittent control

We further study the projective synchronization of a new hyperchaotic system. Different from the most existing methods, intermittent control is applied to chaotic synchronization in the present paper. We formulate the intermittent control system that governs the dynamics of the projective synchronization error, then derive the sufficient conditions for the exponential stability of intermittent control system by using the Lyapunov stability theory, and finally establish the periodically intermittent controller according to the stability criterion by which the projective synchronization is expected to be achieved. The analytical results are also demonstrated by several numerical simulations.     

Passive control and synchronization of hyperchaotic Chen system

This paper investigates the control and synchronization of hyperchaotic Chen system based on the passive theory. By using two outputs, novel passive controllers are respectively designed to realize the globally asymptotical stability of the hyperchaotic Chen system and the error dynamical system, which avoids mistakes in Ref.[11], where function W（z） cannot guarantee that fo（z） is globally asymptotically stable via only one output and W（z） is the Lyapunov function of f0（z）. Furthermore, numerical simulations are given to show the effectiveness of our method.     

Projective synchronization of hyperchaotic system via periodically intermittent control

We further study the projective synchronization of a new hyperchaotic system. Different from the most existing methods, intermittent control is applied to chaotic synchronization in the present paper. We formulate the intermittent control system that governs the dynamics of the projective synchronization error, then derive the sufficient conditions for the exponential stability of intermittent control system by using Lyapunov stability theory, and finally establish the periodically intermittent controller according to the stability criterion by which the projective synchronization is expected to be achieved. The analytical results are also demonstrated by several numerical simulations.     

Liu混沌系统的线性反馈同步控制及电路实验的研究

研究了新型混沌系统——Liu混沌系统的同步控制问题，基于Liu混沌系统的混沌特性，采用线性反馈控制方法，给出了实现Liu混沌系统同步的控制参数取值范围，数值仿真和电路实验证实了该方法的有效性. 关键词： Liu混沌系统 线性反馈控制 混沌同步 电路     

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     

A new four-dimensional hyperchaotic Lorenz system and its adaptive control

Based on the Lorenz chaotic system, this paper constructs a new four-dimensional hyperchaotic Lorenz system, and studies the basic dynamic behaviours of the system. The Routh--Hurwitz theorem is applied to derive the stability conditions of the proposed system. Furthermore, based on Lyapunov stability theory, an adaptive controller is designed and the new four-dimensional hyperchaotic Lorenz system is controlled at equilibrium point. Numerical simulation results are presented to illustrate the effectiveness of this method.     

Adaptive control and synchronization of an uncertain new hyperchaotic Lorenz system

This paper is involved with the adaptive control and synchronization problems for an uncertain new hyperchaotic Lorenz system. Based on the Lyapunov stability theory, the adaptive control law is derived such that the trajectory of hyperchaotic Lorenz system with unknown parameters can be globally stabilized to an unstable equilibrium point of the uncontrolled system. Furthermore, an adaptive control approach is presented to the synchronizations between two identical hyperchaotic systems, particularly between two different uncertain hyperchaotic systems. Numerical simulations show the effectiveness of the presented method.     

超混沌振荡器的混沌耦合同步

提出了两种应用单变量单向混沌耦合同步超混沌振荡器的同步方案。首先给出了混沌耦合同步方案的数学证明，然后通过数值仿真证实了该混沌耦合同步方案的正确性和有效性。最后通过计算条件李雅谱诺夫指数，比较了不同耦合强度下，两种混沌耦合同步和典型的连续耦合同步的同步性能。计算表明在一定的耦合强度下，混沌耦合比典型的连续耦合同步速度快。     

统一超混沌系统的投影同步

利用两种方法研究了统一超混沌系统的同步问题.首先以全状态混合投影自适应同步方法,基于Lyapunov稳定性理论,设计了自适应控制器,理论证明了该控制器可以实现参数已知的统一超混沌系统的全状态混合映射同步.其次使用主动控制同步方法,设计了同步控制器,实现了统一超混沌系统的完全同步,最后数值仿真实验进一步验证了所提出方案的有效性. 关键词： 统一超混沌系统 自适应控制器 全状态混合投影同步 主动控制同步     

超混沌Chen系统和超混沌Roessler系统的异结构同步

用两种不同的方法——主动控制同步法和自适应控制同步法实现超混沌Chen系统和超混沌Roessler系统的异结构同步，各自设计了不同的控制器，使得响应系统与驱动系统同步．当参数已知时，采用主动控制法，方法简单有效且不需要构造Lyapunov函数，实现同步的时间短；当系统参数未知或结构不确定时，基于Lyapunov稳定性理论，给出自适应同步控制器的系统设计过程和参数自适应律，使得系统达到同步同时识别未知参数，数值模拟验证了两种方法的有效性。     

Modified impulsive synchronization of fractional order hyperchaotic systems

In this paper, a modified impulsive control scheme is proposed to realize the complete synchronization of fractional order hyperchaotic systems. By constructing a suitable response system, an integral order synchronization error system is obtained. Based on the theory of Lyapunov stability and the impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of the synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the fixed impulsive distances and control gains. Compared with the existing results, the main results in this paper are practical and rigorous. Simulation results show the effectiveness and the feasibility of the proposed impulsive control method.     

Adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems

In this paper, the adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems with unknown Lipschitz constant is investigated. Firstly, based on the adaptive control theory and the impulsive differential equations theory, the impulsive controller, the adaptive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, the new sufficient criterion is derived to guarantee the asymptotical stability of synchronization error system by the Lyapunov stability theory and the generalized Barbalat's lemma. In addition, numerical simulations demonstrate the effectiveness and feasibility of the proposed adaptive impulsive control method.     

基于改进脉冲控制方法的超混沌系统同步

针对一类整数阶与分数阶超混沌系统的同步问题, 分别提出了改进的脉冲同步方法. 基于Lyapunov稳定性理论与脉冲微分方程理论, 给出超混沌系统一组新的全局渐近同步判据. 特别地, 当脉冲间距与脉冲控制增益为常数时, 可获得更为简单和实用的同步判据. 与现有结果相比, 所得充分条件更次保守且更为实用. 通过对超混沌Chen系统同步的数值仿真研究, 验证了所提方法的有效性和可行性.     

新的切换四涡卷超混沌系统及其电路实现

构建了新的包含2个子系统的切换四涡卷超混沌系统,2个子系统之间既相互关联又相互切换.分析了2个子系统的分岔图、平衡点的稳定性、Lyapunov指数以及动力学行为的演化过程.设计了实现切换四涡卷超混沌系统的电路,系统以时间依赖和状态依赖两种切换律进行任意切换和自主切换,仅用一个电路就能实现2个子系统的切换功能.     

Liu混沌系统的混沌分析及电路实验的研究

研究了一种新型混沌系统——Liu混沌系统的基本动力学行为以及电路实现的问题，给出了相图、庞卡莱映射、功率谱以及李雅普诺夫指数，基于李雅普诺夫指数谱和分叉图分析了系统参数对Liu混沌系统的影响.最后设计硬件电路证实了Liu混沌系统以及Liu混沌系统随系统参数变化时的各种状态的存在.给出数值仿真和电路实验的结果. 关键词： Liu混沌系统 分岔 电路实验