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
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
A new image encryption approach is proposed.First,a sort transformation based on nonlinear chaoticalgorithm is used to shuffle the positions of image pixels.Then the states of hyper-chaos are used to change the greyva...A new image encryption approach is proposed.First,a sort transformation based on nonlinear chaoticalgorithm is used to shuffle the positions of image pixels.Then the states of hyper-chaos are used to change the greyvalues of the shuffled image according to the changed chaotic values of the same position between the above nonlinearchaotic sequence and the sorted chaotic sequence.The experimental results demonstrate that the image encryptionscheme based on a shuffling map shows advantages of large key space and high-level security.Compared with someencryption algorithms,the suggested encryption scheme is more secure.展开更多
This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and extern...This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.展开更多
A secure encryption scheme for color images based on channel fusion and spherical diffraction is proposed in this paper. In the proposed encryption scheme, a channel fusion technology based on the discrete wavelet tra...A secure encryption scheme for color images based on channel fusion and spherical diffraction is proposed in this paper. In the proposed encryption scheme, a channel fusion technology based on the discrete wavelet transformation is used to transform color images into single-channel grayscale images, firstly. In the process of transformation, the hyperchaotic system is used to permutate and diffuse the information of red–green–blue(RGB) channels to reduce the correlation of channels. Then the fused image is encrypted by spherical diffraction transform. Finally, the complex-valued diffraction result is decomposed into two real parts by the improved equal module decomposition, which are the ciphertext and the private key. Compared with the traditional color image encryption schemes that encrypt RGB channels separately, the proposed scheme is highly secure and robust.展开更多
This paper introduces a hyperchaotic system from the Lü system with a sinuso<span style="white-space:nowrap;">ï</span>dal perturbation. This hyperchaotic system has more complex dyn...This paper introduces a hyperchaotic system from the Lü system with a sinuso<span style="white-space:nowrap;">ï</span>dal perturbation. This hyperchaotic system has more complex dynamical behaviors, and can generate 2-scroll hyperchaotic attractor and 2-scroll chaotic attractor under different control parameters. Theoretical analyses and simulation are conducted to investigate the dynamical behaviors of the proposed hyperchaotic system by means of Lyapunov exponents, analysis of the bifurcation diagram and phase portraits.展开更多
In this paper we study the chaos synchronization and anti-synchronization problems between two hyper-chaotic systems with bidirectional coupling,and present synchronization and anti-synchronization methods of chaotic ...In this paper we study the chaos synchronization and anti-synchronization problems between two hyper-chaotic systems with bidirectional coupling,and present synchronization and anti-synchronization methods of chaotic systems,based on timedelayed feedback.Coupling coefficients between the drive and response systems are different,which are supposed to be nonlinearly coupled.Based on the nonlinear control theory,the synchronization and anti-synchronization between two different time-delay hyper-chaotic systems are investigated.The condition of synchronization is derived according to the error dynamical systems.Numerical simulations show the effectiveness and feasibility of the proposed synchronous conditions.展开更多
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.
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 Research Fond for the Doctoral of Higher Education of China,the Hunan Natural Science Foundation under Grant No.05JJ30121the Scientific Research Fund of Hunan Provincial Education Department under Grant No.08B011Educational Research Fund of Hunan Provincial Education Department under Grant No.09C013
文摘A new image encryption approach is proposed.First,a sort transformation based on nonlinear chaoticalgorithm is used to shuffle the positions of image pixels.Then the states of hyper-chaos are used to change the greyvalues of the shuffled image according to the changed chaotic values of the same position between the above nonlinearchaotic sequence and the sorted chaotic sequence.The experimental results demonstrate that the image encryptionscheme based on a shuffling map shows advantages of large key space and high-level security.Compared with someencryption algorithms,the suggested encryption scheme is more secure.
文摘This paper proposes a novel adaptive sliding mode control(SMC) method for synchronization of non-identical fractional-order(FO) chaotic and hyper-chaotic systems. Under the existence of system uncertainties and external disturbances,finite-time synchronization between two FO chaotic and hyperchaotic systems is achieved by introducing a novel adaptive sliding mode controller(ASMC). Here in this paper, a fractional sliding surface is proposed. A stability criterion for FO nonlinear dynamic systems is introduced. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem. To tackle the uncertainties and external disturbances, appropriate adaptation laws are introduced. Particle swarm optimization(PSO) is used for estimating the controller parameters. Finally, finite-time synchronization of the FO chaotic and hyper-chaotic systems is applied to secure communication.
基金Project supported by the National Natural Science Foundation of China (Grant No. U1933132)the Chengdu Science and Technology Program, Sichuan Province, China (Grant No. 2019-GH02-00070-HZ)。
文摘A secure encryption scheme for color images based on channel fusion and spherical diffraction is proposed in this paper. In the proposed encryption scheme, a channel fusion technology based on the discrete wavelet transformation is used to transform color images into single-channel grayscale images, firstly. In the process of transformation, the hyperchaotic system is used to permutate and diffuse the information of red–green–blue(RGB) channels to reduce the correlation of channels. Then the fused image is encrypted by spherical diffraction transform. Finally, the complex-valued diffraction result is decomposed into two real parts by the improved equal module decomposition, which are the ciphertext and the private key. Compared with the traditional color image encryption schemes that encrypt RGB channels separately, the proposed scheme is highly secure and robust.
文摘This paper introduces a hyperchaotic system from the Lü system with a sinuso<span style="white-space:nowrap;">ï</span>dal perturbation. This hyperchaotic system has more complex dynamical behaviors, and can generate 2-scroll hyperchaotic attractor and 2-scroll chaotic attractor under different control parameters. Theoretical analyses and simulation are conducted to investigate the dynamical behaviors of the proposed hyperchaotic system by means of Lyapunov exponents, analysis of the bifurcation diagram and phase portraits.
基金Supported by Scientific and Technological Research Project of The Education Department Henan Province(12B110012)
文摘In this paper we study the chaos synchronization and anti-synchronization problems between two hyper-chaotic systems with bidirectional coupling,and present synchronization and anti-synchronization methods of chaotic systems,based on timedelayed feedback.Coupling coefficients between the drive and response systems are different,which are supposed to be nonlinearly coupled.Based on the nonlinear control theory,the synchronization and anti-synchronization between two different time-delay hyper-chaotic systems are investigated.The condition of synchronization is derived according to the error dynamical systems.Numerical simulations show the effectiveness and feasibility of the proposed synchronous conditions.
