This paper investigates the boundedness of a kind of hyper-chaotic systems that have wide applications in the secure communications. In particular, an accurate bound esti- mation is attained for this kind of hyper-cha...This paper investigates the boundedness of a kind of hyper-chaotic systems that have wide applications in the secure communications. In particular, an accurate bound esti- mation is attained for this kind of hyper-chaotic systems. Then, the result is applied to the chaos synchronization. Some numerical simulations are also given to verify the corresponding theoretical results.展开更多
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 th...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.展开更多
By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lü system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only ...By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lü system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyper-chaotic system, which may be less than any other four-dimensional continuous autonomous hyper-chaotic systems generated by three-dimensional （3D） continuous autonomous chaotic systems. The hyper-chaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lü system when parameter k varies. Although the hyper-chaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyper-chaotic 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.展开更多
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 va...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.展开更多
This paper brings attention on the hybrid synchronization of the Chen hyper-chaotic system by using some simple controllers. We give the sufficient conditions for achieving the goal by using the Lyapunov stability the...This paper brings attention on the hybrid synchronization of the Chen hyper-chaotic system by using some simple controllers. We give the sufficient conditions for achieving the goal by using the Lyapunov stability theory, and we verify our conclusion by numerical simulations.展开更多
The memristor is a kind of non-linear element with memory function,which can be applied to chaotic systems to increase signal randomness and complexity.In this paper,a new four-dimensional hyper-chaotic system is desi...The memristor is a kind of non-linear element with memory function,which can be applied to chaotic systems to increase signal randomness and complexity.In this paper,a new four-dimensional hyper-chaotic system is designed based on a flux controlled memristor model,which can generate complex chaotic attractors.The basic dynamic theory analysis and numerical simulations of the system,such as the stability of equilibrium points,the Lyapunov exponents and dimension,Poincare maps,the power spectrum,and the waveform graph prove that it has rich dynamic behaviors.Then,the circuit implementation of this system is established.The consistency of simulation program with integrated circuit emphasis(SPICE)simulation and numerical analysis proves the ability to generate chaos.Finally,a new image encryption scheme is designed by using the memristor-based hyper-chaotic system proposed in this paper.The scheme involves a total of two encryptions.By using different security analysis factors,the proposed algorithm is compared with other image encryption schemes,including correlation analysis,information entropy,etc.The results show that the proposed image encryption scheme has a large key space and presents a better encryption effect.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1100118911071266)+1 种基金the Natural Science Foundation Project of CQ CSTC(Grant No.2010BB9218)the Fundamental Research Funds for the Central Universities(Grant No.CDJXS11100026)
文摘This paper investigates the boundedness of a kind of hyper-chaotic systems that have wide applications in the secure communications. In particular, an accurate bound esti- mation is attained for this kind of hyper-chaotic systems. Then, the result is applied to the chaos synchronization. Some numerical simulations are also given to verify the corresponding theoretical results.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.61403395)the Natural Science Foundation of Tianjin,China(Grant No.13JCYBJC39000)+3 种基金the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry of Chinathe Fund from the Tianjin Key Laboratory of Civil Aircraft Airworthiness and Maintenance in Civil Aviation of China(Grant No.104003020106)the National Basic Research Program of China(Grant No.2014CB744904)the Fund for the Scholars of Civil Aviation University of China(Grant No.2012QD21x)
文摘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.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60774088 and 10772135)the Research Foundation from the Ministry of Education of China (Grant No. 107024)+2 种基金the Program for New Century Excellent Talents in University of China (NCET)the Application Base and Frontier Technology Project of Tianjin, China (Grant No.08JCZDJC21900)the Scientific Research Foundation for the Returned Overseas Scholars of the State Education Ministry
文摘By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lü system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyper-chaotic system, which may be less than any other four-dimensional continuous autonomous hyper-chaotic systems generated by three-dimensional （3D） continuous autonomous chaotic systems. The hyper-chaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lü system when parameter k varies. Although the hyper-chaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyper-chaotic 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.
基金supported by the National Natural Science Foundation of China(Grant Nos.10772135 and 60874028)the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.11202148)+2 种基金the Incentive Funding of the National Research Foundation of South Africa(GrantNo.IFR2009090800049)the Eskom Tertiary Education Support Programme of South Africathe Research Foundation of Tianjin University of Science and Technology
文摘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.
文摘This paper brings attention on the hybrid synchronization of the Chen hyper-chaotic system by using some simple controllers. We give the sufficient conditions for achieving the goal by using the Lyapunov stability theory, and we verify our conclusion by numerical simulations.
基金Project supported by the National Key Research and Development Program of China (Grant No. 2018YFB1306600)the National Natural Science Foundation of China (Grant Nos. 62076207 and 62076208)the Fundamental Science and Advanced Technology Research Foundation of Chongqing, China (Grant Nos. cstc2017jcyj BX0050)
文摘The memristor is a kind of non-linear element with memory function,which can be applied to chaotic systems to increase signal randomness and complexity.In this paper,a new four-dimensional hyper-chaotic system is designed based on a flux controlled memristor model,which can generate complex chaotic attractors.The basic dynamic theory analysis and numerical simulations of the system,such as the stability of equilibrium points,the Lyapunov exponents and dimension,Poincare maps,the power spectrum,and the waveform graph prove that it has rich dynamic behaviors.Then,the circuit implementation of this system is established.The consistency of simulation program with integrated circuit emphasis(SPICE)simulation and numerical analysis proves the ability to generate chaos.Finally,a new image encryption scheme is designed by using the memristor-based hyper-chaotic system proposed in this paper.The scheme involves a total of two encryptions.By using different security analysis factors,the proposed algorithm is compared with other image encryption schemes,including correlation analysis,information entropy,etc.The results show that the proposed image encryption scheme has a large key space and presents a better encryption effect.
基金the National Natural Science Foundation (Project No. 50475109)Natural Science Foundation of Gansu Province, Government of China (Project No. 3ZS051-A25-030, 3ZS-042-B25-049).
