Applications of modularized circuit designs in a new hyper-chaotic system circuit implementation

Modularized circuit designs for chaotic systems are introduced in this paper.Especially,a typical improved modularized design strategy is proposed and applied to a new hyper-chaotic system circuit implementation.In this paper,the detailed design procedures are described.Multisim simulations and physical experiments are conducted,and the simulation results are compared with Matlab simulation results for different system parameter pairs.These results are consistent with each other and they verify the existence of the hyper-chaotic attractor for this new hyper-chaotic system.

Circuit realization of the fractional-order unified chaotic system

This paper studies the chaotic behaviours of the fractional-order unified chaotic system. Based on the approximation method in frequency domain, it proposes an electronic circuit model of tree shape to realize the fractional-order operator. According to the tree shape model, an electronic circuit is designed to realize the 2.7-order unified chaotic system. Numerical simulations and circuit experiments have verified the existence of chaos in the fraction-order unified system.

Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system

In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.

Dynamical analysis and circuit simulation of a new three-dimensional chaotic system

This paper reports a new three-dimensional autonomous chaotic system. It contains six control parameters and three nonlinear terms. Two cross-product terms are respectively in two equations. And one square term is in the third equation. Basic dynamic properties of the new system are investigated by means of theoretical analysis, numerical simulation, sensitivity to initial, power spectrum, Lyapunov exponent, and Poincar~ diagrams. The dynamic properties affected by variable parameters are also analysed. Finally, the chaotic system is simulated by circuit. The results verify the existence and implementation of the system.

Controlling Liu Chaotic System with Feedback Method and Its Circuit Realization

In the paper, the Liu system with a feedback controller is discussed. The influence of the feedback coefficient of the controlled system is studied through Lyapunov exponents spectrum and bifurcation diagram. Various attractors are demonstrated not only by numerical simulations but also by circuit experiments. Only one feedback channel is used in our study, which is useful in communication. The circuit experiments show that our study has significance in practical applications.

Chaos in fractional-order generalized Lorenz system and its synchronization circuit simulation

The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper. A new electronic circuit unit to realize fractional-order operator is proposed. According to the circuit unit, an electronic circuit is designed to realize a 3.8-order generalized Lorenz chaotic system. Furthermore, synchronization between two fractional-order systems is achieved by utilizing a single-variable feedback method. Circuit experiment simulation results verify the effectiveness of the proposed scheme.

Implementation of a novel two-attractor grid multi-scroll chaotic system

This paper proposed a method of generating two attractors in a novel grid multi-scroll chaotic system. Based on a newly generated three-dimensional system, a two-attractor grid multi-scroll attractor system can be generated by adding two triangular waves and a sign function. Some basic dynamical properties, such as equilibrium points, bifurcations, and phase diagrams, were studied. Furthermore, the system was experimentally confirmed by an electronic circuit. The circuit simulation results and numerical simulation results verified the feasibility of this method.

Hyperchaos evolved from the Liu chaotic system

This paper introduces a new hyperchaotic system by adding an additional state into the third-order Liu chaotic system. Some of its basic dynamical properties, such as the hyperchaotic attractor, Lyapunov exponent, fractal dimension and the hyperchaotic attractor evolving into chaotic, periodic, quasi-periodic dynamical behaviours by varying parameter d are studied briefly. Various attractors are illustrated not only by computer simulation but also by conducting an electronic circuit experiment.

Fractional-Order Control for a Novel Chaotic System Without Equilibrium

The control problem is discussed for a chaotic system without equilibrium in this paper.On the basis of the linear mathematical model of the two-wheeled self-balancing robot,a novel chaotic system which has no equilibrium is proposed.The basic dynamical properties of this new system are studied via Lyapunov exponents and Poincar′e map.To further demonstrate the physical realizability of the presented novel chaotic system,a chaotic circuit is designed.By using fractional-order operators,a controller is designed based on the state-feedback method.According to the Gronwall inequality,Laplace transform and Mittag-Leffler function,a new control scheme is explored for the whole closed-loop system.Under the developed control scheme,the state variables of the closed-loop system are controlled to stabilize them to zero.Finally,the numerical simulation results of the chaotic system with equilibrium and without equilibrium illustrate the effectiveness of the proposed control scheme.

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 new multi-scroll chaotic system

This paper proposes a new simple autonomous chaotic system which can generate multi-scroll chaotic attractors. The characteristic of this new multi-scroll chaotic system is that the 4n ＋ 2rn ＋ 4-scroll chaotic attractors are generated easily with n and m vaxying under n ≤ m. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on EWB （Electronics Workbench）.

Forming and implementing a hyperchaotic system with rich dynamics

A simple three-dimensional （3D） autonomous chaotic system is extended to four-dimensions so as to generate richer nonlinear dynamics. The new system not only inherits the dynamical characteristics of its parental 3D system but also exhibits many new and complex dynamics, including assembled 1-scroll, 2-scroll and 4-scroll attractors, as well as hyperchaotic attractors, by simply tuning a single system parameter. Lyapunov exponents and bifurcation diagrams are obtained via numerical simulations to further justify the existences of chaos and hyperchaos. Finally, an electronic circuit is constructed to implement the system, with experimental and simulation results presented and compared for demonstration and verification.

A new theorem to synchronization of unified chaotic systems via adaptive control

Chaos synchronization has been applied in secure communication, chemicalreaction, biological systems, and information processing. A new theorem to synchronization ofunified chaotic systems via adaptive control is proposed. The constructive theorem provides thedesign scheme for adaptive controller such that a respond system can synchronize with respect to anuncertain drive system. One example for discontinuous chaotic system is proposed to illustrate theeffectiveness and feasibility.

忆阻Sprott-R混沌系统的复杂动态分析与电路实现

基于Sprott-R三维混沌系统,提出了一个具有多稳态和调幅特性的简单四维忆阻混沌系统。首先分析了系统的稳定性,发现该系统具有无穷多个不稳定平衡点。进而利用Lyapunov指数谱、分岔图及相平面图,研究了该忆阻混沌系统的复杂动力学行为特性。研究结果表明,当系统参数发生变化时,系统会经反倍周期分岔由混沌态进入周期态;在不同初始条件下,系统能产生三种共存吸引子,分别为双混沌吸引子共存、周期极限环与混沌吸引子共存、双周期极限环共存;当初始条件变化时,系统输出四维混沌信号的幅度均发生变化。最后,对该系统进行了电路设计与仿真,验证了该忆阻混沌系统的存在性。

新型四维六翼混沌系统仿真电路设计及图像加密应用

针对图像加密困难,信息容易泄露等问题,通过理论计算和模拟仿真,提出一种四维六翼混沌系统结合DNA算法的图像加密方法。该系统具有丰富的动力学特性,进行了系统李雅普诺夫指数、分岔图、功率谱图及平衡点稳定性等关键参数计算分析。其次,搭建了仿真试验电路,并应用Multisim14软件进行了模拟分析,结果显示所提出的混沌系统电路具备良好的混沌动力学能力,以及电路精简、实用等特点。此外,主要从3个方面,包括信息熵、灰度直方图以及相邻像素相关性进行了计算,分析该方法在图像加密方面的作用,结果表明,其保密安全性能较高。

蔡氏电路的非线性动力学探析

针对基尔霍夫电压定律、基尔霍夫电流定律及各元器件的特性,提出了一种基于新型三阶忆阻器的蔡氏电路.并建立一个新型蔡氏电路的数学模型.利用该模型,得出相轨迹图、Lyapunov指数图、Poincaré截面图和分岔图.对基于新型三阶忆阻器的蔡氏电路的非线性动力学特性进行分析表明,该忆阻器的蔡氏电路具有更复杂、更丰富的混沌现象与非线性动力学行为.研究结果可为相关混沌电路、图像加密等提供参考.

一种新型四维三参数混沌指数系统及其电路实现

本文研究了一种新的四维三参数混沌指数系统及其电路实现.首先,通过理论分析和数值仿真,研究该系统的基本动力学行为,如系统不变性和耗散性、平衡点稳定性、Lyapunov指数谱和分岔图等性质,结果表明该系统具有丰富的动力学特性.其次,利用Simulink软件进行电路仿真,仿真结果与数值分析结果一致,从而验证了新四维混沌系统电路实现的可行性,为指数混沌系统应用于电路设计提供了实验基础.

吸引子共存的四维多稳态混沌系统及同步电路

文中设计了一种具有多翼吸引子的四维混沌系统,通过改变系统的多组参数,观察到吸引子结构由四翼变为双翼。采用相图、Lyapunov指数谱、分岔图和复杂度等方法,验证系统的动力学特性。结果表明,通过改变系统参数和选择不同的初始值,系统呈现出极性相反但结构相似的吸引子共存现象。使用Multisim仿真软件进行了电路仿真,发现数值分析和模拟仿真结果一致,验证了系统的可实现性。最后,采用线性反馈同步法对该系统进行了同步控制,并成功实现了同步电路仿真。所设计系统具有丰富的多稳态特性,主从系统在极短的时间内达到了同步,同步效果良好,可广泛应用于保密通信领域。

A novel multi-scroll chaotic generator:Analysis, simulation, and implementation

Based on a new three-dimensional autonomous linear system and designing a specific form of saturated function series and a sign function with two variables of system, which are employed to increase saddle-focus equilibrium points with index 2, a novel multi-scroll chaotic system is proposed and its typical dynamical characteristics including bifurcation diagram, Poincare map, and the stability of equilibrium points are analyzed. The hardware circuit is designed and the experimental results are presented for confirmation.

The analysis of complex behaviours of a novel three dimensional autonomous system

This paper introduces a new three dimensional autonomous system with five equilibrium points. It demonstrates complex chaotic behaviours within a wide range of parameters, which are described by phase portraits, Lyapunov exponents, frequency spectrum, etc. Analysis of the bifurcation and Poincar@ map is used to reveal mechanisms of generating these complicated phenomena. The corresponding electronic circuits are designed, exhibiting experimental chaotic attractors in accord with numerical simulations. Since frequency spectrum analysis shows a broad frequency bandwidth, this system has perspective of potential applications in such engineering fields as secure communication.