In this paper we propose a novel four-dimensional fractional order hyperchaotic system derived from a Liu system.Electronics workbench（EWB） and Matlab simulations show the dynamical behavior of the proposed four-dim...In this paper we propose a novel four-dimensional fractional order hyperchaotic system derived from a Liu system.Electronics workbench（EWB） and Matlab simulations show the dynamical behavior of the proposed four-dimensional fractional order hyperchaotic system.Finally,after separately using EWB and Matlab,an electronic circuit is designed to realize the novel four-dimensional fractional order hyperchaotic system and the experimental circuit results are obtained which are identical to software simulations.展开更多
This paper is concerned with the Hopf bifurcation control of a new hyperchaotic circuit system.Thestability of the hyperchaotic circuit system depends on a selected control parameter is studied,and the critical value ...This paper is concerned with the Hopf bifurcation control of a new hyperchaotic circuit system.Thestability of the hyperchaotic circuit system depends on a selected control parameter is studied,and the critical value ofthe system parameter at which Hopf bifurcation occurs is investigated.Theoretical analysis give the stability of the Hopfbifurcation.In particular,washout filter aided feedback controllers are designed for delaying the bifurcation point andensuring the stability of the bifurcated limit cycles.An important feature of the control laws is that they do not resultin any change in the set of equilibria.Computer simulation results are presented to confirm the analytical predictions.展开更多
This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively...This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors＇ knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach.展开更多
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...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.展开更多
This study introduces a new continuous time differential system,which contains ten terms with three quadratic nonlinearities.The new system can demonstrate hyperchaotic,chaotic,quasi-periodic,and periodic behaviors fo...This study introduces a new continuous time differential system,which contains ten terms with three quadratic nonlinearities.The new system can demonstrate hyperchaotic,chaotic,quasi-periodic,and periodic behaviors for its different parameter values.All theoretical and numerical analysis are investigated to confirm the complex hyperchaotic behavior of our proposed model using many tools that include Kaplan-Yorke dimension,equilibrium points stability,bifurcation diagrams,and Lyapunov exponents.By means of Multisim software,the authors also designed an electronic circuit to confirm our proposed systems’physical feasibility.MATLAB and Multisim simulation results excellently agree with each other,which validate the feasibility of our new ten terms hyperchaotic system and make it very desirable to use in different domains especially in chaotic-based communication.Furthermore,by employing the drive response synchronisation,we developed a secure communication strategy for the proposed system.Findings from the proposed scheme show that the proposed approach was successful in completing the encryption and decryption procedure.展开更多
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 in...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.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 51177117)the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100201110023)
文摘In this paper we propose a novel four-dimensional fractional order hyperchaotic system derived from a Liu system.Electronics workbench（EWB） and Matlab simulations show the dynamical behavior of the proposed four-dimensional fractional order hyperchaotic system.Finally,after separately using EWB and Matlab,an electronic circuit is designed to realize the novel four-dimensional fractional order hyperchaotic system and the experimental circuit results are obtained which are identical to software simulations.
基金Supported by the National Natural Science Foundation of China under Grant No.10672053
文摘This paper is concerned with the Hopf bifurcation control of a new hyperchaotic circuit system.Thestability of the hyperchaotic circuit system depends on a selected control parameter is studied,and the critical value ofthe system parameter at which Hopf bifurcation occurs is investigated.Theoretical analysis give the stability of the Hopfbifurcation.In particular,washout filter aided feedback controllers are designed for delaying the bifurcation point andensuring the stability of the bifurcated limit cycles.An important feature of the control laws is that they do not resultin any change in the set of equilibria.Computer simulation results are presented to confirm the analytical predictions.
基金Project supported by the National Natural Science Foundation of China(Grant No.61403143)the Natural Science Foundation of Guangdong Province,China(Grant No.2014A030313739)+1 种基金the Science and Technology Foundation Program of Guangzhou City,China(Grant No.201510010124)the Excellent Doctorial Dissertation Foundation of Guangdong Province,China(Grant No.XM080054)
文摘This paper aims at developing a novel method of constructing a class of multi-wing chaotic and hyperchaotic system by introducing a unified step function. In order to overcome the essential difficulties in iteratively adjusting multiple parameters of conventional multi-parameter control, this paper introduces a unified step function controlled by a single parameter for constructing various multi-wing chaotic and hyperchaotic systems. In particular, to the best of the authors＇ knowledge, this is also the first time to find a non-equilibrium multi-wing hyperchaotic system by means of the unified step function control. According to the heteroclinic loop Shilnikov theorem, some properties for multi-wing attractors and its chaos mechanism are further discussed and analyzed. A circuit for multi-wing systems is designed and implemented for demonstration, which verifies the effectiveness of the proposed approach.
文摘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.
文摘This study introduces a new continuous time differential system,which contains ten terms with three quadratic nonlinearities.The new system can demonstrate hyperchaotic,chaotic,quasi-periodic,and periodic behaviors for its different parameter values.All theoretical and numerical analysis are investigated to confirm the complex hyperchaotic behavior of our proposed model using many tools that include Kaplan-Yorke dimension,equilibrium points stability,bifurcation diagrams,and Lyapunov exponents.By means of Multisim software,the authors also designed an electronic circuit to confirm our proposed systems’physical feasibility.MATLAB and Multisim simulation results excellently agree with each other,which validate the feasibility of our new ten terms hyperchaotic system and make it very desirable to use in different domains especially in chaotic-based communication.Furthermore,by employing the drive response synchronisation,we developed a secure communication strategy for the proposed system.Findings from the proposed scheme show that the proposed approach was successful in completing the encryption and decryption procedure.
文摘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.
