Discrete-time chaotic circuit implementations of a tent map and a Bernoulli map using switched-current （SI） techniques are presented. The two circuits can be constructed with 16 MOSFET＇s and 2 capacitors. The simul...Discrete-time chaotic circuit implementations of a tent map and a Bernoulli map using switched-current （SI） techniques are presented. The two circuits can be constructed with 16 MOSFET＇s and 2 capacitors. The simulations and experiments built with commercially available IC＇s for the circuits have demonstrated the validity of the circuit designs. The experiment results also indicate that the proposed circuits are integrable by a standard CMOS technology. The implementations are useful for studies and applications of chaos.展开更多
This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide...This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization.展开更多
The influence of parameter mismatches on multirhythmic patterns in chains of coupled Rossler circuits are explored experimentally. The parameter mismatches in coupled chaotic oscillators are found to help form a kind ...The influence of parameter mismatches on multirhythmic patterns in chains of coupled Rossler circuits are explored experimentally. The parameter mismatches in coupled chaotic oscillators are found to help form a kind of multirhythmic pattern as reported in chains of biological coupled oscillators [Phys. Rev. Lett. 92 228102]. Moreover, a new type of multirhythmic pattern based on the envelope of time series is observed.展开更多
We present a generalized analytical solution to the normalized state equations of a class of coupled simple secondorder non-autonomous circuit systems. The analytical solutions thus obtained are used to study the sync...We present a generalized analytical solution to the normalized state equations of a class of coupled simple secondorder non-autonomous circuit systems. The analytical solutions thus obtained are used to study the synchronization dynamics of two different types of circuit systems, differing only by their constituting nonlinear element. The synchronization dynamics of the coupled systems is studied through two-parameter bifurcation diagrams, phase portraits, and time-series plots obtained from the explicit analytical solutions. Experimental figures are presented to substantiate the analytical results. The generalization of the analytical solution for other types of coupled simple chaotic systems is discussed. The synchronization dynamics of the coupled chaotic systems studied through two-parameter bifurcation diagrams obtained from the explicit analytical solutions is reported for the first time.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
A two-SBT-memristor-based chaotic circuit was proposed. The stability of the equilibrium point was studied by theoretical analysis. The close dependence of the circuit dynamic characteristics on its initial conditions...A two-SBT-memristor-based chaotic circuit was proposed. The stability of the equilibrium point was studied by theoretical analysis. The close dependence of the circuit dynamic characteristics on its initial conditions and circuit parameters was investigated by utilizing Lyapunov exponents spectra, bifurcation diagrams, phase diagrams, and Poincaré maps. The analysis showed that the circuit system had complex dynamic behaviors, such as stable points, period, chaos, limit cycles,and so on. In particular, the chaotic circuit produced the multistability phenomenon, such as coexisting attractors and coexisting periods.展开更多
We evaluate the influence of temperature on the behavior of a three-phase clock-driven metal–oxide–semiconductor （MOS） chaotic circuit. The chaotic circuit consists of two nonlinear functions, a level shifter, and...We evaluate the influence of temperature on the behavior of a three-phase clock-driven metal–oxide–semiconductor （MOS） chaotic circuit. The chaotic circuit consists of two nonlinear functions, a level shifter, and three sample and hold blocks. It is necessary to analyze a CMOS-based chaotic circuit with respect to variation in temperature for stability because the circuit is sensitive to the behavior of the circuit design parameters. The temperature dependence of the proposed chaotic circuit is investigated via the simulation program with integrated circuit emphasis （SPICE） using 0.6-μm CMOS process technology with a 5-V power supply and a 20-kHz clock frequency. The simulation results demonstrate the effects of temperature on the chaotic dynamics of the proposed chaotic circuit. The time series, frequency spectra, bifurcation phenomena, and Lyapunov exponent results are provided.展开更多
Aimed at the generation of high-quality test set in the shortest possible time, the test generation for combinational circuits （CC） based on the chaotic particle swarm optimization （CPSO） algorithm is presented ac...Aimed at the generation of high-quality test set in the shortest possible time, the test generation for combinational circuits （CC） based on the chaotic particle swarm optimization （CPSO） algorithm is presented according to the analysis of existent problems of CC test generation, and an appropriate CPSO algorithm model has been constructed. With the help of fault simulator, the test set of ISCAS＇ 85 benchmark CC is generated using the CPSO, and some techniques are introduced such as half-random generation, and simulation of undetected fauhs.with original test vector, and inverse test vector. Experimental results show that this algorithm can generate the same fault coverage and small-size test set in short time compared with other known similar methods, which proves that the proposed method is applicable and effective.展开更多
In the paper, the Liu system with a feedback controller is discussed. The influence of the feedback coefficient of the controlled system is studied through Lyapunov exponents spectrum and bifurcation diagram. Various ...In the paper, the Liu system with a feedback controller is discussed. The influence of the feedback coefficient of the controlled system is studied through Lyapunov exponents spectrum and bifurcation diagram. Various attractors are demonstrated not only by numerical simulations but also by circuit experiments. Only one feedback channel is used in our study, which is useful in communication. The circuit experiments show that our study has significance in practical applications.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
We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry, especially in the frame of chaotic attractors for solving practical problems(generating ...We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry, especially in the frame of chaotic attractors for solving practical problems(generating hyperchaos; developing chaos based pseudo random number generator(CPRNG) and chaotic multistream PRNG; secure communication via synchronization). They can also be used in cryptography, generic algorithms in optimization, control, etc.展开更多
Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis...Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis methods, stability analysis of the equilibrium set of the circuit is performed, the distribution of stable and unstable regions corresponding to the memristor initial states is achieved, and the complex dynamical behaviors of the circuit depending on the circuit parameters and the memristor initial states are investigated. The theoretical analysis and numerical simulation results demonstrate that the proposed chaotic circuit with two memristors has an equilibrium set located on the plane constituted by the inner state variables of two memristors. The stability of the equilibrium set depends on both the circuit parameters and the initial states of the two memristors. Rich nonlinear dynamical phenomena, such as state transitions, transient hyperchaos and so on, are expected.展开更多
A chaotic system with various equilibrium types has rich dynamic behaviors.Its state can switch flexibly among different families of attractors,which is beneficial to the practical applications.So it has been widely c...A chaotic system with various equilibrium types has rich dynamic behaviors.Its state can switch flexibly among different families of attractors,which is beneficial to the practical applications.So it has been widely concerned in recent years.In this paper,a new 5D hyper-chaotic system is proposed.The important characteristic of the system is that it may have multiple types of equilibrium points by changing system parameters,namely,linear equilibrium point,no equilibrium point,non-hyperbolic unstable equilibrium point and stable hyperbolictype equilibrium point.Furthermore,there are hyper-chaotic phenomena and multi-stability about the coexistence of multiple chaotic attractors and the coexistence of hyper-chaotic attractors and chaotic attractors in the system.In addition,the system,complexity is analyzed.It is found that the complexity is close to 1 in the hyper-chaotic state and a pseudo-random sequence generated by the system passes all the statistical tests.Finally,an analog circuit of the system is designed and simulated.展开更多
基金Supported by the National Natural Science Foundation of China (No.60372004) and Natural Science Foundation of Guangdong Province (No.20820)
文摘Discrete-time chaotic circuit implementations of a tent map and a Bernoulli map using switched-current （SI） techniques are presented. The two circuits can be constructed with 16 MOSFET＇s and 2 capacitors. The simulations and experiments built with commercially available IC＇s for the circuits have demonstrated the validity of the circuit designs. The experiment results also indicate that the proposed circuits are integrable by a standard CMOS technology. The implementations are useful for studies and applications of chaos.
基金Project supported by the National Natural Science Foundation of China(Grant Nos 60774088 and 10772135)the Foundation of the Application Base and Frontier Technology Research Project of Tianjin,China (Grant Nos 07JCZDJC09600,08JCZDJC21900 and 08JCZDJC18600)the Tianjin Key Laboratory for Control Theory & Applications in Complicated Industry Systems of China
文摘This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11262006 and 11062002)the Science and Technology Project of Jiangxi Province,China(Grant Nos.GJJ12330 and 2010GQW0021)
文摘The influence of parameter mismatches on multirhythmic patterns in chains of coupled Rossler circuits are explored experimentally. The parameter mismatches in coupled chaotic oscillators are found to help form a kind of multirhythmic pattern as reported in chains of biological coupled oscillators [Phys. Rev. Lett. 92 228102]. Moreover, a new type of multirhythmic pattern based on the envelope of time series is observed.
文摘We present a generalized analytical solution to the normalized state equations of a class of coupled simple secondorder non-autonomous circuit systems. The analytical solutions thus obtained are used to study the synchronization dynamics of two different types of circuit systems, differing only by their constituting nonlinear element. The synchronization dynamics of the coupled systems is studied through two-parameter bifurcation diagrams, phase portraits, and time-series plots obtained from the explicit analytical solutions. Experimental figures are presented to substantiate the analytical results. The generalization of the analytical solution for other types of coupled simple chaotic systems is discussed. The synchronization dynamics of the coupled chaotic systems studied through two-parameter bifurcation diagrams obtained from the explicit analytical solutions is reported for the first time.
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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61703247 and 61703246)the Qingdao Science and Technology Plan Project, China (Grant No. 19-6-2-2-cg)the Elite Project of Shandong University of Science and Technology, and the Taishan Scholar Project of Shandong Province of China
文摘A two-SBT-memristor-based chaotic circuit was proposed. The stability of the equilibrium point was studied by theoretical analysis. The close dependence of the circuit dynamic characteristics on its initial conditions and circuit parameters was investigated by utilizing Lyapunov exponents spectra, bifurcation diagrams, phase diagrams, and Poincaré maps. The analysis showed that the circuit system had complex dynamic behaviors, such as stable points, period, chaos, limit cycles,and so on. In particular, the chaotic circuit produced the multistability phenomenon, such as coexisting attractors and coexisting periods.
基金Project supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(Grant No.2011-0011698)
文摘We evaluate the influence of temperature on the behavior of a three-phase clock-driven metal–oxide–semiconductor （MOS） chaotic circuit. The chaotic circuit consists of two nonlinear functions, a level shifter, and three sample and hold blocks. It is necessary to analyze a CMOS-based chaotic circuit with respect to variation in temperature for stability because the circuit is sensitive to the behavior of the circuit design parameters. The temperature dependence of the proposed chaotic circuit is investigated via the simulation program with integrated circuit emphasis （SPICE） using 0.6-μm CMOS process technology with a 5-V power supply and a 20-kHz clock frequency. The simulation results demonstrate the effects of temperature on the chaotic dynamics of the proposed chaotic circuit. The time series, frequency spectra, bifurcation phenomena, and Lyapunov exponent results are provided.
文摘Aimed at the generation of high-quality test set in the shortest possible time, the test generation for combinational circuits （CC） based on the chaotic particle swarm optimization （CPSO） algorithm is presented according to the analysis of existent problems of CC test generation, and an appropriate CPSO algorithm model has been constructed. With the help of fault simulator, the test set of ISCAS＇ 85 benchmark CC is generated using the CPSO, and some techniques are introduced such as half-random generation, and simulation of undetected fauhs.with original test vector, and inverse test vector. Experimental results show that this algorithm can generate the same fault coverage and small-size test set in short time compared with other known similar methods, which proves that the proposed method is applicable and effective.
文摘In the paper, the Liu system with a feedback controller is discussed. The influence of the feedback coefficient of the controlled system is studied through Lyapunov exponents spectrum and bifurcation diagram. Various attractors are demonstrated not only by numerical simulations but also by circuit experiments. Only one feedback channel is used in our study, which is useful in communication. The circuit experiments show that our study has significance in practical applications.
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.
文摘We introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry, especially in the frame of chaotic attractors for solving practical problems(generating hyperchaos; developing chaos based pseudo random number generator(CPRNG) and chaotic multistream PRNG; secure communication via synchronization). They can also be used in cryptography, generic algorithms in optimization, control, etc.
基金supported by the National Natural Science Foundation of China (Grant No. 60971090)the Natural Science Foundations of Jiangsu Province, China (Grant No. BK2009105)
文摘Based on Chua’s chaotic oscillation circuit, a fifth-order chaotic circuit with two memristors is designed and its corresponding dimensionless mathematic model is established. By using conventional dynamical analysis methods, stability analysis of the equilibrium set of the circuit is performed, the distribution of stable and unstable regions corresponding to the memristor initial states is achieved, and the complex dynamical behaviors of the circuit depending on the circuit parameters and the memristor initial states are investigated. The theoretical analysis and numerical simulation results demonstrate that the proposed chaotic circuit with two memristors has an equilibrium set located on the plane constituted by the inner state variables of two memristors. The stability of the equilibrium set depends on both the circuit parameters and the initial states of the two memristors. Rich nonlinear dynamical phenomena, such as state transitions, transient hyperchaos and so on, are expected.
基金the Science Foundation of Ministry of Education of China(No.02152)。
文摘A chaotic system with various equilibrium types has rich dynamic behaviors.Its state can switch flexibly among different families of attractors,which is beneficial to the practical applications.So it has been widely concerned in recent years.In this paper,a new 5D hyper-chaotic system is proposed.The important characteristic of the system is that it may have multiple types of equilibrium points by changing system parameters,namely,linear equilibrium point,no equilibrium point,non-hyperbolic unstable equilibrium point and stable hyperbolictype equilibrium point.Furthermore,there are hyper-chaotic phenomena and multi-stability about the coexistence of multiple chaotic attractors and the coexistence of hyper-chaotic attractors and chaotic attractors in the system.In addition,the system,complexity is analyzed.It is found that the complexity is close to 1 in the hyper-chaotic state and a pseudo-random sequence generated by the system passes all the statistical tests.Finally,an analog circuit of the system is designed and simulated.
