In this paper, a novel four dimensional hyper-chaotic system is coined based on the Chen system, which contains two quadratic terms and five system parameters. The proposed system can generate a hyper-chaotic attracto...In this paper, a novel four dimensional hyper-chaotic system is coined based on the Chen system, which contains two quadratic terms and five system parameters. The proposed system can generate a hyper-chaotic 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 hyper-cha^tic system can generate complex dynamical behaviors, e.g., a direct transition from quasi-periodic behavior to hyper-chaotic behavior. Finally, an electronic circuit is designed to implement the hyper-chaotic system, the experimental results are consist with the numerical simulations, which verifies the existence of the hyper-chaotic attractor. Due to the complex dynamic behaviors, this new hyper-cha^tic system is useful in the secure communication.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
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
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
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
基金Project supported by the Natural Science Foundation of China (Grant Nos.61174094, 50977063, and 60904063)the Foundation of the Application Base and Frontier Technology Research Project of Tianjin, China (Grant No.10JCZDJC23100)the Development of Science and Technology Foundation of the Higher Education Institutions of Tianjin, China (Grant No.20080826)
文摘In this paper, a novel four dimensional hyper-chaotic system is coined based on the Chen system, which contains two quadratic terms and five system parameters. The proposed system can generate a hyper-chaotic 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 hyper-cha^tic system can generate complex dynamical behaviors, e.g., a direct transition from quasi-periodic behavior to hyper-chaotic behavior. Finally, an electronic circuit is designed to implement the hyper-chaotic system, the experimental results are consist with the numerical simulations, which verifies the existence of the hyper-chaotic attractor. Due to the complex dynamic behaviors, this new hyper-cha^tic system is useful in the secure communication.
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.
