1.

Implementation of a novel twoattractor grid multiscroll chaotic system





罗小华 涂正伟 刘希瑞 蔡昌 梁亦龙 龚璞《中国物理 B》,2010年第19卷第7期


This paper proposed a method of generating two attractors in a novel grid multiscroll chaotic system.Based on a newly generated threedimensional system,a twoattractor grid multiscroll 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.

2.

A new multiscroll chaotic system





王发强 刘崇新《中国物理》,2006年第15卷第12期


This paper proposes a new simple autonomous chaotic system which can generate multiscroll chaotic attractors. The characteristic of this new multiscroll chaotic system is that the 4n ＋ 2rn ＋ 4scroll 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）.

3.

A new multiscroll chaotic generator





王发强 刘崇新《中国物理》,2007年第16卷第4期


In this paper a new simple multiscroll chaotic generator is studied. The characteristic of this new multiscroll chaotic generator is that it is easy to generate different number of scroll chaotic attractors through modifying the nature number n after fixing the suitable system parameters and it does not need complex mathematical derivation. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on Electronic Workbench （EWB）.

4.

Multiscroll hidden attractors and multiwing hidden attractors in a 5dimensional memristive system





《中国物理 B》,2017年第11期


A novel 5dimensional(5D) memristive chaotic system is proposed, in which multiscroll hidden attractors and multiwing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multiscroll hidden attractors and multiwing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multiscroll hidden attractors and multiwing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincar′e map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones.

5.

Generation and synchronization of Nscroll chaotic and hyperchaotic attractors in fourthorder systems





禹思敏 马在光 丘水生 彭世国 林清华《中国物理》,2004年第13卷第3期


Based on our previous works and Lyapunov stability theory, this paper studies the generation and synchronization of Nscroll chaotic and hyperchaotic attractors in fourthorder systems. A fourthorder circuit, by introducing additional breakpoints in the modified Chua oscillator, is implemented for the study of generation and synchronization of Nscroll chaotic attractors.This confirms the consistency of theoretical calculation, numerical simulation and circuit experiment.Furthermore,we give a refined and extended study of generating and synchronizing Nscroll hyperchaotic attractors in the fourthorder MCK system and report the new theoretical result, which is verified by computer simulations.

6.

Passive control of a 4scroll chaotic system





王发强 刘崇新《中国物理》,2007年第16卷第4期


This paper studies the control of a new chaotic system which can generate 4scroll attractors. Based on the properties of a passive system, it derives the essential conditions under which this new chaotic system could be equivalent to a passive system and globally asymptotically stabilize at a zero equilibrium point via smooth state feedback. Simulation results and circuit experiment show that the proposed chaos control method is effective.

7.

Design and implementation of a novel multiscroll chaotic system 被引次数：2





张朝霞 禹思敏《中国物理 B》,2009年第18卷第1期


This paper proposes a novel approach for generating a multiscroll chaotic system.Together with the theoretical design and numerical simulations,three different types of attractor are available,governed by constructing triangular wave,sawtooth wave and hysteresis sequence.The presented new multiscroll chaotic system is different from the classical multiscroll chaotic Chua system in dimensionless state equations,nonlinear functions and maximum Lyapunov exponents.In addition,the basic dynamical behaviours,including equilibrium points,eigenvalues,eigenvectors,eigenplanes,bifurcation diagrams and Lyapunov exponents,are further investigated.The success of the design is illustrated by both numerical simulations and circuit experiments.

8.

Adaptive generalized synchronization between Chen system and a multiscroll chaotic system





谌龙 史跃东 王德石《中国物理 B》,2010年第19卷第10期


Based on Lyapunov theory, the adaptive generalized synchronization between Chen system and a multiscroll chaotic system is investigated. According to the form of target function a proper adaptive controller is designed, by which the controlled Chen system can be synchronized with a multiscroll chaotic system including unknown parameters. The Lyapunov direct method is exploited to prove that the synchronization error and parameter identification error both converge to zero. Numerical simulation results verify the feasibility of the proposed method further.

9.

Pitchfork bifurcation and circuit implementation of a novel Chen hyperchaotic system





董恩增 陈增强 陈在平 倪建云《中国物理 B》,2012年第3期


In this paper,a novel four dimensional hyperchaotic system is coined based on the Chen system,which contains two quadratic terms and five system parameters.The proposed system can generate a hyperchaotic attractor in wide parameters regions.By using the center manifold theorem and the local bifurcation theory,a pitchfork bifurcation is demonstrated to arise at the zero equilibrium point.Numerical analysis demonstrates that the hyperchaotic system can generate complex dynamical behaviors,e.g.,a direct transition from quasiperiodic behavior to hyperchaotic behavior.Finally,an electronic circuit is designed to implement the hyperchaotic system,the experimental results are consist with the numerical simulations,which verifies the existence of the hyperchaotic attractor.Due to the complex dynamic behaviors,this new hyperchaotic system is useful in the secure communication.

10.

Design and FPGA implementation of multiwing chaotic switched systems based on a quadratic transformation





石擎宇 黄霞 袁方 李玉霞《中国物理 B》,2021年第2期


Based on a quadratic transformation and a switching function,a novel multiwing chaotic switched system is proposed.First,a 4wing chaotic system is constructed from a 2wing chaotic system on the basis of a quadratic transformation.Then,a switching function is designed and by adjusting the switching function,the number and the distribution of the saddlefocus equilibrium points of the switched system can be regulated.Thus,a set of chaotic switched systems,which can produce 6to81216wing attractors,are generated.The Lyapunov exponent spectra,bifurcation diagrams,and Poincarémaps are given to verify the existence of the chaotic attractors.Besides,the digital circuit of the multiwing chaotic switched system is designed by using the Verilog HDL fixedpoint algorithm and the state machine control.Finally,the multiwing chaotic attractors are demonstrated via FPGA platform.The experimental results show that the number of the wings of the chaotic attractors can be expanded more effectively with the combination of the quadratic transformation and the switching function methods.

11.

Analysis and implementation of new fractionalorder multiscroll hidden attractors





崔力 雒文辉 欧青立《中国物理 B》,2021年第2期


To improve the complexity of chaotic signals,in this paper we first put forward a new threedimensional quadratic fractionalorder multiscroll hidden chaotic system,then we use the Adomian decomposition algorithm to solve the proposed fractionalorder chaotic system and obtain the chaotic phase diagrams of different orders,as well as the Lyaponov exponent spectrum,bifurcation diagram,and SE complexity of the 0.99order system.In the process of analyzing the system,we find that the system possesses the dynamic behaviors of hidden attractors and hidden bifurcations.Next,we also propose a method of using the Lyapunov exponents to describe the basins of attraction of the chaotic system in the matlab environment for the first time,and obtain the basins of attraction under different order conditions.Finally,we construct an analog circuit system of the fractionalorder chaotic system by using an equivalent circuit module of the fractionalorder integral operators,thus realizing the 0.9order multiscroll hidden chaotic attractors.

12.

Chaos in fractionalorder generalized Lorenz system and its synchronization circuit simulation 被引次数：1





张若洵 杨世平《中国物理 B》,2009年第18卷第8期


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

13.

Applications of modularized circuit designs in a new hyperchaotic system circuit implementation





王蕊 孙辉 王杰智 王鲁 王晏超《中国物理 B》,2015年第24卷第2期


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 hyperchaotic 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 hyperchaotic attractor for this new hyperchaotic system.

14.

Bifurcation and dynamics in doubledelayed Chua circuits with periodic perturbation





杨文杰《中国物理 B》,2022年第2期


Rank1 attractors play a vital role in biological systems and the circuit systems.In this paper,we consider a periodically kicked Chua model with two delays in a circuit system.We first analyze the local stability of the equilibria of the Chua system and obtain the existence conditions of supercritical Hopf bifurcations.Then,we derive some explicit formulas about Hopf bifurcation,which could help us find the form of Hopf bifurcation and the stability of bifurcating period solutions through the Hassards method.Also,we show that rank1 chaos occurs when the Chua model with two delays undergoes a supercritical Hopf bifurcation and encounters a periodic kick,which shows the effect of two delays on the circuit system.Finally,we illustrate the theoretical analysis by simulations and try to explain the mechanism of delay in our system.

15.

Passive control of chaotic system with multiple strange attractors 被引次数：2





宋运忠 赵光宙 齐冬莲《中国物理》,2006年第15卷第10期


In this paper we present a new simple controller for a chaotic system, that is, the NewtonLeipnik equation with two strange attractors： the upper attractor （UA） and the lower attractor （LA）. The controller design is based on the passive technique. The final structure of this controller for original stabilization has a simple nonlinear feedback form. Using a passive method, we prove the stability of a closedloop system. Based on the controller derived from the passive principle, we investigate three different kinds of chaotic control of the system, separately： the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intraattractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one, and the interattractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the suggested method.

16.

Generating one,two,threeand fourscroll attractors from a novel fourdimensional smooth autonomous chaotic system





SaraDadras HamidRezaMomeni《中国物理 B》,2010年第19卷第6期


A new fourdimensional quadratic smooth autonomous chaotic system is presented in this paper,which can exhibit periodic orbit and chaos under the conditions on the system parameters.Importantly,the system can generate one,two,threeand fourscroll chaotic attractors with appropriate choices of parameters.Interestingly,all the attractors are generated only by changing a single parameter.The dynamic analysis approach in the paper involves time series,phase portraits,Poincar’e maps,a bifurcation diagram,and Lyapunov exponents,to investigate some basic dynamical behaviours of the proposed fourdimensional system.

17.

A novel one equilibrium hyperchaotic system generated upon Lü attractor





贾红艳 陈增强 袁著祉《中国物理 B》,2010年第19卷第2期


By introducing an additional state feedback into a threedimensional autonomous chaotic attractor Lü system, this paper presents a novel fourdimensional continuous autonomous hyperchaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyperchaotic system, which may be less than any other fourdimensional continuous autonomous hyperchaotic systems generated by threedimensional (3D) continuous autonomous chaotic systems. The hyperchaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lü system when parameter k varies. Although the hyperchaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyperchaotic attractor can be observed. A circuit is also designed when parameter k varies and the results of the circuit experiment are in good agreement with those of simulation.

18.

Nonlinear feedback control of a novel hyperchaotic system and its circuit implementation 被引次数：1





汪浩祥 蔡国梁 缪盛 田立新《中国物理 B》,2010年第19卷第3期


This paper reports a new hyperchaotic system by adding an additional state variable into a threedimensional 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,quasiperiodic 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.

19.

The openplusclosed loop （OPCL） method for chaotic systems with multiple strange attractors





宋运忠《中国物理》,2007年第16卷第7期


Based on the openplusclosedloop （OPCL） control method a systematic and comprehensive controller is presented in this paper for a chaotic system, that is, the NewtonLeipnik equation with two strange attractors： the upper attractor （UA） and the lower attractor （LA）. Results show that the final structure of the suggested controller for stabilization has a simple linear feedback form. To keep the integrity of the suggested approach, the globality proof of the basins of entrainment is also provided. In virtue of the OPCL technique, three different kinds of chaotic controls of the system are investigated, separately： the original control forcing the chaotic motion to settle down to the origin from an arbitrary position of the phase space; the chaotic intraattractor control for stabilizing the equilibrium points only belonging to the upper chaotic attractor or the lower chaotic one; and the interattractor control for compelling the chaotic oscillation from one basin to another one. Both theoretical analysis and simulation results verify the validity of the proposed means.

20.

Spectrum Analysis and Circuit Implementation of a New 3D Chaotic System with Novel Chaotic Attractors





董高高 郑松 田立新 杜瑞瑾《中国物理快报》,2010年第2期


The new autonomous system with only three equilibrium points is introduced. This system does not belong to the generalized Lorenz systems. The novel attractors are observed over a large range of parameters, which have rarely been reported in previous work. As an important component in chaotic signal generators, a physical circuit has been designed. The experimental results are in agreement with numerical simulations. More significantly, spectral analysis shows that the system has an extremely broad frequency spectral bandwidth in 0131.6 Hz, without investigating any possible electronic techniques, which is more desirable for secure communications.
