In this paper, chaotic behaviours in the fractional-order Liu system are studied. Based on the approximation theory of fractional-order operator, circuits are designed to simulate the fractional- order Liu system with...In this paper, chaotic behaviours in the fractional-order Liu system are studied. Based on the approximation theory of fractional-order operator, circuits are designed to simulate the fractional- order Liu system with q=0.1 - 0.9 in a step of 0.1, and an experiment has demonstrated the 2.7-order Liu system. The simulation results prove that the chaos exists indeed in the fractional-order Liu system with an order as low as 0.3. The experimental results prove that the fractional-order chaotic system can be realized by using hardware devices, which lays the foundation for its practical applications.展开更多
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
A new circuit unit for the analysis and the synthesis of the chaotic behaviours in a fractional-order Liu system is proposed in this paper. Based on the approximation theory of fractional-order operator, an electronic...A new circuit unit for the analysis and the synthesis of the chaotic behaviours in a fractional-order Liu system is proposed in this paper. Based on the approximation theory of fractional-order operator, an electronic circuit is designed to describe the dynamic behaviours of the fractional-order Liu system with α = 0.9. The results between simulation and experiment are in good agreement with each other, thereby proving that the chaos exists indeed in the fractional-order Liu system.展开更多
This paper studies the chaotic behaviours of the fractional-order unified chaotic system. Based on the approximation method in frequency domain, it proposes an electronic circuit model of tree shape to realize the fra...This paper studies the chaotic behaviours of the fractional-order unified chaotic system. Based on the approximation method in frequency domain, it proposes an electronic circuit model of tree shape to realize the fractional-order operator. According to the tree shape model, an electronic circuit is designed to realize the 2.7-order unified chaotic system. Numerical simulations and circuit experiments have verified the existence of chaos in the fraction-order unified system.展开更多
In this paper a new hyperchaotic system is reported. Some basic dynamical properties, such as continuous spectrum, Lyapunov exponents, fractal dimensions, strange attractor and Poincare mapping of the new hyperchaotic...In this paper a new hyperchaotic system is reported. Some basic dynamical properties, such as continuous spectrum, Lyapunov exponents, fractal dimensions, strange attractor and Poincare mapping of the new hyperchaotic system are studied. Dynamical behaviours of the new hyperchaotic system are proved by not only numerical simulation and brief theoretical analysis but also an electronic circuit experiment.展开更多
A novel four-dimensional autonomous hyperchaotic system is reported in this paper. Some basic dynamical properties of the new hyperchaotic system are investigated in detail by means of a continuous spectrum, Lyapunov ...A novel four-dimensional autonomous hyperchaotic system is reported in this paper. Some basic dynamical properties of the new hyperchaotic system are investigated in detail by means of a continuous spectrum, Lyapunov exponents, fractional dimensions, a strange attractor and Poincar~ mapping. The dynamical behaviours of the new hyperchaotic system are proved by not only performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit experiment.展开更多
Avariable scale-convex-peak method is constructed to identify the frequency of weak harmonic signal. The key of this method is to find a set of optimal identification coefficients to make the transition of dynamic beh...Avariable scale-convex-peak method is constructed to identify the frequency of weak harmonic signal. The key of this method is to find a set of optimal identification coefficients to make the transition of dynamic behavior topologically persistent. By the stochastic Melnikov method, the lower bound of the chaotic threshold continuous function is obtained in the mean-square sense.The intermediate value theorem is applied to detect the optimal identification coefficients. For the designated identification system, there is a valuable co-frequency-convex-peak in bifurcation diagram, which indicates the state transition of chaosperiod-chaos. With the change of the weak signal amplitude and external noise intensity in a certain range, the convex peak phenomenon is still maintained, which leads to the identification of frequency. Furthermore, the proposition of the existence of reversible scaling transformation is introduced to detect the frequency of the harmonic signal in engineering. The feasibility of constructing the hardware and software platforms of the variable scale-convex-peak method is verified by the experimental results of circuit design and the results of early fault diagnosis of actual bearings, respectively.展开更多
文摘In this paper, chaotic behaviours in the fractional-order Liu system are studied. Based on the approximation theory of fractional-order operator, circuits are designed to simulate the fractional- order Liu system with q=0.1 - 0.9 in a step of 0.1, and an experiment has demonstrated the 2.7-order Liu system. The simulation results prove that the chaos exists indeed in the fractional-order Liu system with an order as low as 0.3. The experimental results prove that the fractional-order chaotic system can be realized by using hardware devices, which lays the foundation for its practical applications.
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.
文摘A new circuit unit for the analysis and the synthesis of the chaotic behaviours in a fractional-order Liu system is proposed in this paper. Based on the approximation theory of fractional-order operator, an electronic circuit is designed to describe the dynamic behaviours of the fractional-order Liu system with α = 0.9. The results between simulation and experiment are in good agreement with each other, thereby proving that the chaos exists indeed in the fractional-order Liu system.
文摘This paper studies the chaotic behaviours of the fractional-order unified chaotic system. Based on the approximation method in frequency domain, it proposes an electronic circuit model of tree shape to realize the fractional-order operator. According to the tree shape model, an electronic circuit is designed to realize the 2.7-order unified chaotic system. Numerical simulations and circuit experiments have verified the existence of chaos in the fraction-order unified system.
文摘In this paper a new hyperchaotic system is reported. Some basic dynamical properties, such as continuous spectrum, Lyapunov exponents, fractal dimensions, strange attractor and Poincare mapping of the new hyperchaotic system are studied. Dynamical behaviours of the new hyperchaotic system are proved by not only numerical simulation and brief theoretical analysis but also an electronic circuit experiment.
文摘A novel four-dimensional autonomous hyperchaotic system is reported in this paper. Some basic dynamical properties of the new hyperchaotic system are investigated in detail by means of a continuous spectrum, Lyapunov exponents, fractional dimensions, a strange attractor and Poincar~ mapping. The dynamical behaviours of the new hyperchaotic system are proved by not only performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit experiment.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11872253, 11602151, 11790282)the Natural Science Foundation for Outstanding Young Researcher in Hebei Province of China(Grant No. A2017210177)+2 种基金the Natural Science Foundation in Hebei Province of China (Grant No. A2019421005)the Hundred Excellent Innovative Talents in Hebei Province (Grant No. SLRC2019037)the Basic Research Team Special Support Projects (Grant No. 311008)。
文摘Avariable scale-convex-peak method is constructed to identify the frequency of weak harmonic signal. The key of this method is to find a set of optimal identification coefficients to make the transition of dynamic behavior topologically persistent. By the stochastic Melnikov method, the lower bound of the chaotic threshold continuous function is obtained in the mean-square sense.The intermediate value theorem is applied to detect the optimal identification coefficients. For the designated identification system, there is a valuable co-frequency-convex-peak in bifurcation diagram, which indicates the state transition of chaosperiod-chaos. With the change of the weak signal amplitude and external noise intensity in a certain range, the convex peak phenomenon is still maintained, which leads to the identification of frequency. Furthermore, the proposition of the existence of reversible scaling transformation is introduced to detect the frequency of the harmonic signal in engineering. The feasibility of constructing the hardware and software platforms of the variable scale-convex-peak method is verified by the experimental results of circuit design and the results of early fault diagnosis of actual bearings, respectively.