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
A new five-dimensional fractional-order laser chaotic system(FOLCS)is constructed by incorporating complex variables and fractional calculus into a Lorentz-Haken-type laser system.Dynamical behavior of the system,circ...A new five-dimensional fractional-order laser chaotic system(FOLCS)is constructed by incorporating complex variables and fractional calculus into a Lorentz-Haken-type laser system.Dynamical behavior of the system,circuit realization and application in pseudorandom number generators are studied.Many types of multi-stable states are discovered in the system.Interestingly,there are two types of state transition phenomena in the system,one is the chaotic state degenerates to a periodical state,and the other is the intermittent chaotic oscillation.In addition,the complexity of the system when two parameters change simultaneously is measured by the spectral entropy algorithm.Moreover,a digital circuit is design and the chaotic oscillation behaviors of the system are verified on this circuit.Finally,a pseudo-random sequence generator is designed using the FOLCS,and the statistical characteristics of the generated pseudo-random sequence are tested with the NIST-800-22.This study enriches the research on the dynamics and applications of FOLCS.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
The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper. A new electronic circuit unit to realize fractional-order operator is proposed. According to th...The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper. A new electronic circuit unit to realize fractional-order operator is proposed. According to the circuit unit, an electronic circuit is designed to realize a 3.8-order generalized Lorenz chaotic system. Furthermore, synchronization between two fractional-order systems is achieved by utilizing a single-variable feedback method. Circuit experiment simulation results verify the effectiveness of the proposed scheme.展开更多
The control problem is discussed for a chaotic system without equilibrium in this paper.On the basis of the linear mathematical model of the two-wheeled self-balancing robot,a novel chaotic system which has no equilib...The control problem is discussed for a chaotic system without equilibrium in this paper.On the basis of the linear mathematical model of the two-wheeled self-balancing robot,a novel chaotic system which has no equilibrium is proposed.The basic dynamical properties of this new system are studied via Lyapunov exponents and Poincar′e map.To further demonstrate the physical realizability of the presented novel chaotic system,a chaotic circuit is designed.By using fractional-order operators,a controller is designed based on the state-feedback method.According to the Gronwall inequality,Laplace transform and Mittag-Leffler function,a new control scheme is explored for the whole closed-loop system.Under the developed control scheme,the state variables of the closed-loop system are controlled to stabilize them to zero.Finally,the numerical simulation results of the chaotic system with equilibrium and without equilibrium illustrate the effectiveness of the proposed control scheme.展开更多
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.
基金Project supported by the National Natural Science Foundation of China(Grant No.62061014)the Natural Science Foundation of Liaoning Province,China(Grant No.2020-MS-274)。
文摘A new five-dimensional fractional-order laser chaotic system(FOLCS)is constructed by incorporating complex variables and fractional calculus into a Lorentz-Haken-type laser system.Dynamical behavior of the system,circuit realization and application in pseudorandom number generators are studied.Many types of multi-stable states are discovered in the system.Interestingly,there are two types of state transition phenomena in the system,one is the chaotic state degenerates to a periodical state,and the other is the intermittent chaotic oscillation.In addition,the complexity of the system when two parameters change simultaneously is measured by the spectral entropy algorithm.Moreover,a digital circuit is design and the chaotic oscillation behaviors of the system are verified on this circuit.Finally,a pseudo-random sequence generator is designed using the FOLCS,and the statistical characteristics of the generated pseudo-random sequence are tested with the NIST-800-22.This study enriches the research on the dynamics and applications of FOLCS.
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.
基金supported by the Natural Science Foundation of Hebei Province,China (Grant Nos A2008000136 and A2006000128)
文摘The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper. A new electronic circuit unit to realize fractional-order operator is proposed. According to the circuit unit, an electronic circuit is designed to realize a 3.8-order generalized Lorenz chaotic system. Furthermore, synchronization between two fractional-order systems is achieved by utilizing a single-variable feedback method. Circuit experiment simulation results verify the effectiveness of the proposed scheme.
基金supported by the National Natural Science Foundation of China(61573184)Jiangsu Natural Science Foundation of China(SBK20130033)+1 种基金Six Talents Peak Project of Jiangsu Province(2012-XXRJ-010)Fundamental Research Funds for the Central Universities(NE2016101)
文摘The control problem is discussed for a chaotic system without equilibrium in this paper.On the basis of the linear mathematical model of the two-wheeled self-balancing robot,a novel chaotic system which has no equilibrium is proposed.The basic dynamical properties of this new system are studied via Lyapunov exponents and Poincar′e map.To further demonstrate the physical realizability of the presented novel chaotic system,a chaotic circuit is designed.By using fractional-order operators,a controller is designed based on the state-feedback method.According to the Gronwall inequality,Laplace transform and Mittag-Leffler function,a new control scheme is explored for the whole closed-loop system.Under the developed control scheme,the state variables of the closed-loop system are controlled to stabilize them to zero.Finally,the numerical simulation results of the chaotic system with equilibrium and without equilibrium illustrate the effectiveness of the proposed control scheme.
