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.     

一个超混沌系统及其分数阶电路仿真实验

提出了一个新的四维自治超混沌系统，对其基本动力学特性进行了数值仿真和深入的研究.运用EWB软件对实现该超混沌系统的分数阶振荡器电路进行了仿真实验证实. 关键词： 分数阶超混沌系统 动力学行为 分数阶电路     

A novel four-dimensional autonomous hyperchaotic system

A novel four-dimensional autonomous hyperchaotic system is reported in this paper. Some basic dynamical properties of the new hyperchaotic system are investigated in detail by means of a continuous spectrum, Lyapunov exponents, fractional dimensions, a strange attractor and Poincaré mapping. The dynamical behaviours of the new hyperchaotic system are proved by not only performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit experiment.     

基于微控制器数字硬件实现的网格涡卷超混沌系统

基于微控制器(MCU)设计了一个通用的四维混沌系统数字硬件实验电路,由此实现了9×7网格涡卷的混沌和超混沌吸引子的生成.本文基于由Colpitts振荡器模型延伸出的四维多涡卷超混沌系统,通过引入单位锯齿波函数替换原系统中的三角波函数,构建了一个便于MCU数字硬件实现的新的网格涡卷超混沌系统,并对新系统网格涡卷吸引子的形成机理进行了分析和数值仿真.通过采用Euler算法对新系统进行离散化,在实验电路的有效动态范围内可以生成比原系统更多网格涡卷数量的吸引子.实验结果有效验证了本文基于MCU实现的网格涡卷超混沌系统的可行性.     

Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation

This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponents, bifurcation diagram and the hyperchaotic attractor evolving into periodic, quasi-periodic dynamical behaviours by varying parameter k are studied. An effective nonlinear feedback control method is used to suppress hyperchaos to unstable equilibrium. Furthermore, a circuit is designed to realize this new hyperchaotic system by electronic workbench (EWB). Numerical simulations are presented to show these results.     

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.     

一个新的超混沌系统及其自适应追踪控制

通过在一个三维混沌系统中加入状态反馈控制器, 构造出一个新的四维超混沌系统. 分析表明, 随着不同参数变化该系统呈现周期、复杂周期、准周期、混沌及超混沌运动. 同时设计出模拟电子电路对该超混沌系统进行了实验验证. 最后, 设计了一个自适应追踪控制器,实现了其对各种不同参考信号的单变量追踪控制.     

The synchronization of a fractional order hyperchaotic system based on passive control

This paper investigates the synchronization of a fractional order hyperchaotic system using passive control. A passive controller is designed, based on the properties of a passive system. Then the synchronization between two fractional order hyperchaotic systems under different initial conditions is realized, on the basis of the stability theorem for fractional order systems. Numerical simulations and circuitry simulations are presented to verify the analytical results.     

Circuit implementation of a new hyperchaos in fractional-order system

This paper introduces a new four-dimensional （4D） hyperchaotic system, which has only two quadratic nonlinearity parameters but with a complex topological structure. Some complicated dynamical properties are then investigated in detail by using bifurcations, Poincare mapping, LE spectra. Furthermore, a simple fourth-order electronic circuit is designed for hardware implementation of the 4D hyperchaotic attractors. In particular, a remarkable fractional-order circuit diagram is designed for physically verifying the hyperchaotic attractors existing not only in the integer-order system but also in the fractional-order system with an order as low as 3.6.     

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 novel hyperchaotic system and its circuit implementation

A four-dimensional hyperchaotic system with five parameters is proposed. Its dynamical properties such as dissipativity, equilibrium points, Lyapunov exponent, Lyapunov dimension, bifurcation diagrams and Poincare maps are analyzed theoretically and numerically. Theoretical analyses and simulation tests indicate that the new system's dynamics behavior can be periodic attractor, chaotic attractor and hyperchaotic attractor as the parameter varies. Finally, the circuit of this new hyperchaotic system is designed and realized by Multisim software. The simulation results confirm that the chaotic system is different from the existing chaotic systems and is a novel hyperchaotic system. The system is recommendable for many engineering applications such as information processing, cryptology, secure communications, etc.     

超混沌Lorenz系统

对Lorenz系统添加一个非线性控制器，使之构成四维超混沌Lorenz系统.利用分岔图、Lyapunov指数谱及相图分析方法，研究了超混沌Lorenz系统的运动规律.数值模拟结果表明：新引入参数处于不同取值范围时，超混沌Lorenz系统可以分别呈现收敛、发散、周期、混沌及超混沌动力学行为. 关键词： Lorenz系统 超混沌 Lyapunov指数 分岔     

基于Colpitts振荡器模型生成的多涡卷超混沌吸引子

基于三阶单涡卷混沌Colpitts振荡器模型,通过引入两个分段线性三角波函数,构造了一个新型四维多涡卷超混沌系统,生成了(2M+1)×(2N+1),(2M+1)和(2N+1)涡卷混沌和超混沌吸引子.利用相轨图、Poincar啨映射、Lyapunov指数谱和分岔图等方法,对新提出的四维多涡卷超混沌系统进行了动力学分析,结果表明,多涡卷超混沌系统的Hopf分岔点仅与控制参数有关,而涡卷数量和控制参数的混沌和超混沌范围随着转折点数量的增加而增加.此外,设计了一个实现四维多涡卷超混沌系统的模拟电路,实验输出与数值仿真的两个结果基本一致.     

A hyperchaotic system stabilization via inverse optimal control and experimental research

In this paper, some basic dynamical properties of a four-dimensional autonomous hyperchaotic system are investigated by means of Poincar′e mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this new hyperchaotic system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit experiment. An efficient approaching is developed for global asymptotic stabilization of this four-dimensional hyperchaotic system. Based on the method of inverse optimal control for nonlinear systems, a linear state feedback is electronically implemented. It is remarkably simple as compared with other chaos control ways, like nonlinear state feedback.     

新分数阶超混沌系统的研究与控制及其电路实现

为了提高混沌信号的复杂性,提出了一个新的分数阶四维超混沌系统,并对该系统的混沌动力学特性进行详细的理论分析和数值仿真,Maltab仿真证实了该分数阶超混沌系统存在混沌的最小阶数为3.2阶.同时运用Multisim软件对该系统进行电路实验仿真验证.最后设计了简单有效的线性反馈控制器,并进行电路实现,仿真结果证明了控制器是有效的. 关键词： 分数阶超混沌系统 动力学特性 电路仿真 反馈控制     

四维切换超混沌系统

构建了一类关联且有多种切换方式的四维超混沌系统.依据系统的分岔图确定了各个子系统都处于混沌状态时，系统参数的取值范围.分析了这类四维超混沌系统平衡点的性质、超混沌吸引子的相图和Lyapunov指数等特性，设计了实现这类可切换超混沌系统的实际电路，利用系统选择器，一个电路可以实现四个关联子系统的功能. 关键词： 超混沌系统 分岔图 Lyapunov指数 切换     

一个新的超混沌系统

基于一个新三维混沌系统,通过引入非线性控制器,构造出一个新的四维超混沌系统,并对该系统的动力学行为进行了研究,包括它的Lyapunov指数谱、分岔图等.分析表明,新的四维系统随着新引入的参数变化呈现周期、复杂周期、混沌及超混沌动力学行为;设计的硬件电路的实验结果也证实了相关结果. 关键词： 超混沌 Lyapunov指数 分岔图 混沌电路     

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.     

Analysis and implementation of a new hyperchaotic system

Based on a modified Lorenz system, a relatively simple four-dimensional continuous autonomous hyperchaotic system is proposed by introducing a state feedback controller. The system consists of four coupled first-order ordinary differential equations with three nonlinear cross-product terms. Some dynamical properties of this hyperchaotic system, including equlibria, stability, Lyapunov exponent spectrum and bifurcation, are analysed in detail. Moreover, an electronic circuit diagram is designed for demonstrating the existence of the hyperchaos, and verifying computer simulation results.     

Coexisting multiscroll hyperchaotic attractors generated from a novel memristive jerk system

In this paper, two kinds of novel non-ideal voltage-controlled multi-piecewise cubic nonlinearity memristors and their mathematical models are presented. By adding the memristor to the circuit of a three-dimensional jerk system, a novel memristive multiscroll hyperchaotic jerk system is established without introducing any other ordinary nonlinear functions, from which \(2N+2\)-scroll and \(2M+1\)-scroll hyperchaotic attractors are achieved. It is exciting to note that this new memristive system can produce the extreme multistability phenomenon of coexisting infinitely multiple attractors. Furthermore, the dynamical behaviours of the proposed system are analysed by phase portraits, equilibrium points, Lyapunov exponents and bifurcation diagrams. The results indicate that the system exhibits hyperchaotic, chaotic and periodic dynamics. Especially, the phenomenon of transient chaos can also be found in this memristive multiscroll system. Additionally, the MULTISIM circuit simulations and the hardware experimental results are performed to verify numerical simulations.