This paper proposed a method of generating two attractors in a novel grid multi-scroll chaotic system. Based on a newly generated three-dimensional system, a two-attractor grid multi-scroll attractor system can be gen...This paper proposed a method of generating two attractors in a novel grid multi-scroll chaotic system. Based on a newly generated three-dimensional system, a two-attractor grid multi-scroll attractor system can be generated by adding two triangular waves and a sign function. Some basic dynamical properties, such as equilibrium points, bifurcations, and phase diagrams, were studied. Furthermore, the system was experimentally confirmed by an electronic circuit. The circuit simulation results and numerical simulation results verified the feasibility of this method.展开更多
This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by construc...This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by constructing triangular wave, sawtooth wave and hysteresis sequence. The presented new multi-scroll chaotic system is different from the classical multi-scroll chaotic Chua system in dimensionless state equations, nonlinear functions and maximum Lyapunov exponents. In addition, the basic dynamical behaviours, including equilibrium points, eigenvalues, eigenvectors, eigenplanes, bifurcation diagrams and Lyapunov exponents, are further investigated. The success of the design is illustrated by both numerical simulations and circuit experiments.展开更多
Based on the framework of Colpitts oscillator, a four-dimensional multi-scroll hyperchaotic system is proposed, which generates (2M+1)×(2N+1)-scroll chaotic and hyperchaotic attractors. The key strategy is to inc...Based on the framework of Colpitts oscillator, a four-dimensional multi-scroll hyperchaotic system is proposed, which generates (2M+1)×(2N+1)-scroll chaotic and hyperchaotic attractors. The key strategy is to increase the number of index-2 equilibrium points by introducing two unit saw-tooth functions to extend and modify the Colpitts oscillator model. By using bifurcation diagram and phase portrait, the dynamical characteristics of the multi-scroll hyperchaotic system are briefly studied. Moreover, micro-controller based circuit realization is introduced and the experimental results dem-onstrate that 7×5-scroll chaotic and hyperchaotic attractors can be obtained in the digital circuit.展开更多
Combing with the generalized Hamiltonian system theory,by introducing a special form of sinusoidal function,a class of n-dimensional(n=1,2,3)controllable multi-scroll conservative chaos with complicated dynamics is co...Combing with the generalized Hamiltonian system theory,by introducing a special form of sinusoidal function,a class of n-dimensional(n=1,2,3)controllable multi-scroll conservative chaos with complicated dynamics is constructed.The dynamics characteristics including bifurcation behavior and coexistence of the system are analyzed in detail,the latter reveals abundant coexisting flows.Furthermore,the proposed system passes the NIST tests and has been implemented physically by FPGA.Compared to the multi-scroll dissipative chaos,the experimental portraits of the proposed system show better ergodicity,which have potential application value in secure communication and image encryption.展开更多
In this paper a new simple multi-scroll chaotic generator is studied. The characteristic of this new multi-scroll chaotic generator is that it is easy to generate different number of scroll chaotic attractors through ...In this paper a new simple multi-scroll chaotic generator is studied. The characteristic of this new multi-scroll chaotic generator is that it is easy to generate different number of scroll chaotic attractors through modifying the nature number n after fixing the suitable system parameters and it does not need complex mathematical derivation. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on Electronic Workbench （EWB）.展开更多
Based on Lyapunov theory, the adaptive generalized synchronization between Chen system and a multi-scroll chaotic system is investigated. According to the form of target function a proper adaptive controller is design...Based on Lyapunov theory, the adaptive generalized synchronization between Chen system and a multi-scroll chaotic system is investigated. According to the form of target function a proper adaptive controller is designed, by which the controlled Chen system can be synchronized with a multi-scroll chaotic system including unknown parameters. The Lyapunov direct method is exploited to prove that the synchronization error and parameter identification error both converge to zero. Numerical simulation results verify the feasibility of the proposed method further.展开更多
Based on a new three-dimensional autonomous linear system and designing a specific form of saturated function series and a sign function with two variables of system, which are employed to increase saddle-focus equili...Based on a new three-dimensional autonomous linear system and designing a specific form of saturated function series and a sign function with two variables of system, which are employed to increase saddle-focus equilibrium points with index 2, a novel multi-scroll chaotic system is proposed and its typical dynamical characteristics including bifurcation diagram, Poincare map, and the stability of equilibrium points are analyzed. The hardware circuit is designed and the experimental results are presented for confirmation.展开更多
A novel 5-dimensional（5D） memristive chaotic system is proposed, in which multi-scroll hidden attractors and multiwing hidden attractors can be observed on different phase planes. The dynamical system has multiple l...A novel 5-dimensional（5D） memristive chaotic system is proposed, in which multi-scroll hidden attractors and multiwing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multi-scroll hidden attractors and multi-wing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multi-scroll hidden attractors and multi-wing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincar′e map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones.展开更多
This paper proposes a new simple autonomous chaotic system which can generate multi-scroll chaotic attractors. The characteristic of this new multi-scroll chaotic system is that the 4n ＋ 2rn ＋ 4-scroll chaotic attra...This paper proposes a new simple autonomous chaotic system which can generate multi-scroll chaotic attractors. The characteristic of this new multi-scroll chaotic system is that the 4n ＋ 2rn ＋ 4-scroll chaotic attractors are generated easily with n and m vaxying under n ≤ m. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on EWB （Electronics Workbench）.展开更多
A new method is presented to generate two-directional (2D) grid multi-scroll chaotic attractors via a specific form of the sine function and sign function series, which are applied to increase saddle points of index 2...A new method is presented to generate two-directional (2D) grid multi-scroll chaotic attractors via a specific form of the sine function and sign function series, which are applied to increase saddle points of index 2. The scroll number in the x-direction is modified easily through changing the thresholds of the specific form of the sine function, while the scroll number in the y-direction is controlled by the sign function series. Some basic dynamical properties, such as equilibrium points, bifurcation diagram, phase portraits, and Lyapunov exponents spectrum are studied. Furthermore, the electronic circuit of the system is designed and its simulation results are given by Multisim 10.展开更多
A novel memristor-based multi-scroll hyperchaotic system is proposed.Based on a voltage-controlled memristor and a modulating sine nonlinear function,a novel method is proposed to generate the multi-scroll hyperchaoti...A novel memristor-based multi-scroll hyperchaotic system is proposed.Based on a voltage-controlled memristor and a modulating sine nonlinear function,a novel method is proposed to generate the multi-scroll hyperchaotic attractors.Firstly,a multi-scroll chaotic system is constructed from a three-dimensional chaotic system by designing a modulating sine nonlinear function.Then,a voltage-controlled memristor is introduced into the above-designed multi-scroll chaotic system.Thus,a memristor-based multi-scroll hyperchaotic system is generated,and this hyperchaotic system can produce various coexisting hyperchaotic attractors with different topological structures.Moreover,different number of scrolls and different topological attractors can be obtained by varying the initial conditions of this system without changing the system parameters.The Lyapunov exponents,bifurcation diagrams and basins of attraction are given to analyze the dynamical characteristics of the multi-scroll hyperchaotic system.Besides,the field programmable gate array(FPGA)based digital implementation of the memristor-based multi-scroll hyperchaotic system is carried out.The experimental results of the FPGA-based digital circuit are displayed on the oscilloscope.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 60972069)the Science and Technology Foundation of the Education Department of Chongqing (Grant No. KJ090513)
文摘This paper proposed a method of generating two attractors in a novel grid multi-scroll chaotic system. Based on a newly generated three-dimensional system, a two-attractor grid multi-scroll attractor system can be generated by adding two triangular waves and a sign function. Some basic dynamical properties, such as equilibrium points, bifurcations, and phase diagrams, were studied. Furthermore, the system was experimentally confirmed by an electronic circuit. The circuit simulation results and numerical simulation results verified the feasibility of this method.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 60572073 and 60871025)the Natural Science Foundation of Guangdong Province,China (Grant Nos 8151009001000060,5001818 and 8351009001000002)
文摘This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by constructing triangular wave, sawtooth wave and hysteresis sequence. The presented new multi-scroll chaotic system is different from the classical multi-scroll chaotic Chua system in dimensionless state equations, nonlinear functions and maximum Lyapunov exponents. In addition, the basic dynamical behaviours, including equilibrium points, eigenvalues, eigenvectors, eigenplanes, bifurcation diagrams and Lyapunov exponents, are further investigated. The success of the design is illustrated by both numerical simulations and circuit experiments.
基金Supported by the Natural Science Foundations of Jiangsu Province (No. BK2009105)
文摘Based on the framework of Colpitts oscillator, a four-dimensional multi-scroll hyperchaotic system is proposed, which generates (2M+1)×(2N+1)-scroll chaotic and hyperchaotic attractors. The key strategy is to increase the number of index-2 equilibrium points by introducing two unit saw-tooth functions to extend and modify the Colpitts oscillator model. By using bifurcation diagram and phase portrait, the dynamical characteristics of the multi-scroll hyperchaotic system are briefly studied. Moreover, micro-controller based circuit realization is introduced and the experimental results dem-onstrate that 7×5-scroll chaotic and hyperchaotic attractors can be obtained in the digital circuit.
基金Project supported by the Natural Science Foundation of Tianjin,China(Grant No.18JCYBJC87700)the Natural Science Foundation of China(Grant No.61603274)。
文摘Combing with the generalized Hamiltonian system theory,by introducing a special form of sinusoidal function,a class of n-dimensional(n=1,2,3)controllable multi-scroll conservative chaos with complicated dynamics is constructed.The dynamics characteristics including bifurcation behavior and coexistence of the system are analyzed in detail,the latter reveals abundant coexisting flows.Furthermore,the proposed system passes the NIST tests and has been implemented physically by FPGA.Compared to the multi-scroll dissipative chaos,the experimental portraits of the proposed system show better ergodicity,which have potential application value in secure communication and image encryption.
文摘In this paper a new simple multi-scroll chaotic generator is studied. The characteristic of this new multi-scroll chaotic generator is that it is easy to generate different number of scroll chaotic attractors through modifying the nature number n after fixing the suitable system parameters and it does not need complex mathematical derivation. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on Electronic Workbench （EWB）.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50875259)
文摘Based on Lyapunov theory, the adaptive generalized synchronization between Chen system and a multi-scroll chaotic system is investigated. According to the form of target function a proper adaptive controller is designed, by which the controlled Chen system can be synchronized with a multi-scroll chaotic system including unknown parameters. The Lyapunov direct method is exploited to prove that the synchronization error and parameter identification error both converge to zero. Numerical simulation results verify the feasibility of the proposed method further.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51377124 and 51521065)the Foundation for the Author of National Excellent Doctoral Dissertation,China(Grant No.201337)the New Star of Youth Science and Technology of Shaanxi Province,China(Grant No.2016KJXX-40)
文摘Based on a new three-dimensional autonomous linear system and designing a specific form of saturated function series and a sign function with two variables of system, which are employed to increase saddle-focus equilibrium points with index 2, a novel multi-scroll chaotic system is proposed and its typical dynamical characteristics including bifurcation diagram, Poincare map, and the stability of equilibrium points are analyzed. The hardware circuit is designed and the experimental results are presented for confirmation.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51177117 and 51307130)
文摘A novel 5-dimensional（5D） memristive chaotic system is proposed, in which multi-scroll hidden attractors and multiwing hidden attractors can be observed on different phase planes. The dynamical system has multiple lines of equilibria or no equilibrium when the system parameters are appropriately selected, and the multi-scroll hidden attractors and multi-wing hidden attractors have nothing to do with the system equilibria. Particularly, the numbers of multi-scroll hidden attractors and multi-wing hidden attractors are sensitive to the transient simulation time and the initial values. Dynamical properties of the system, such as phase plane, time series, frequency spectra, Lyapunov exponent, and Poincar′e map, are studied in detail. In addition, a state feedback controller is designed to select multiple hidden attractors within a long enough simulation time. Finally, an electronic circuit is realized in Pspice, and the experimental results are in agreement with the numerical ones.
文摘This paper proposes a new simple autonomous chaotic system which can generate multi-scroll chaotic attractors. The characteristic of this new multi-scroll chaotic system is that the 4n ＋ 2rn ＋ 4-scroll chaotic attractors are generated easily with n and m vaxying under n ≤ m. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on EWB （Electronics Workbench）.
文摘A new method is presented to generate two-directional (2D) grid multi-scroll chaotic attractors via a specific form of the sine function and sign function series, which are applied to increase saddle points of index 2. The scroll number in the x-direction is modified easily through changing the thresholds of the specific form of the sine function, while the scroll number in the y-direction is controlled by the sign function series. Some basic dynamical properties, such as equilibrium points, bifurcation diagram, phase portraits, and Lyapunov exponents spectrum are studied. Furthermore, the electronic circuit of the system is designed and its simulation results are given by Multisim 10.
基金the National Natural Sciene Foundation of China(Grant Nos.61973199 and 61973200)the Taishan Scholar Project of Shandong Province of China。
文摘A novel memristor-based multi-scroll hyperchaotic system is proposed.Based on a voltage-controlled memristor and a modulating sine nonlinear function,a novel method is proposed to generate the multi-scroll hyperchaotic attractors.Firstly,a multi-scroll chaotic system is constructed from a three-dimensional chaotic system by designing a modulating sine nonlinear function.Then,a voltage-controlled memristor is introduced into the above-designed multi-scroll chaotic system.Thus,a memristor-based multi-scroll hyperchaotic system is generated,and this hyperchaotic system can produce various coexisting hyperchaotic attractors with different topological structures.Moreover,different number of scrolls and different topological attractors can be obtained by varying the initial conditions of this system without changing the system parameters.The Lyapunov exponents,bifurcation diagrams and basins of attraction are given to analyze the dynamical characteristics of the multi-scroll hyperchaotic system.Besides,the field programmable gate array(FPGA)based digital implementation of the memristor-based multi-scroll hyperchaotic system is carried out.The experimental results of the FPGA-based digital circuit are displayed on the oscilloscope.
