This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to ac...This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.展开更多
A finite-time controller is designed for a class of nonlinear systems subject to sector nonlinear inputs. A novel and simple approach is suggested based on the finite-time control principle. The designed sliding-mode ...A finite-time controller is designed for a class of nonlinear systems subject to sector nonlinear inputs. A novel and simple approach is suggested based on the finite-time control principle. The designed sliding-mode controller can drive a chaotic system to track a smooth target signal in a finite time. The chaotic Duffing-Holmes oscillator is used for verification and demonstration.展开更多
This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under par...This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The. criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincare map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using nomfeedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to periodmotions by adding an excitation term.展开更多
This paper presents a robust output feedback control method for uncertain chaotic systems, which comprises a nonlinear inversion-based controller with a fuzzy robust compensator. The proposed controller eliminates the...This paper presents a robust output feedback control method for uncertain chaotic systems, which comprises a nonlinear inversion-based controller with a fuzzy robust compensator. The proposed controller eliminates the unknown nonlinear function by using a fuzzy system, whose inputs are not the state variables but feedback error signals. The underlying stability analysis as well as parameter update law design are carried out by using the Lyapunov-based technique. The proposed method indicates that the nonlinear inversion-based control approach can also be applied to uncertain chaotic systems. Theoretical results are illustrated through two simulation examples.展开更多
In this paper,determination of the characteristics of futures market in China is presented by the method of the phase-randomized surrogate data.There is a significant difference in the obtained critical values when th...In this paper,determination of the characteristics of futures market in China is presented by the method of the phase-randomized surrogate data.There is a significant difference in the obtained critical values when this method is used for random timeseries and for nonlinear chaotic timeseries.The singular value decomposition is used to reduce noise in the chaotic timeseries.The phase space of chaotic timeseries is decomposed into range space and null noise space.The original chaotic timeseries in range space is restructured.The method of strong disturbance based on the improved general constrained randomized method is further adopted to re-deternination.With the calculated results,an analysis on the trend of futures market of commodity is made in this paper.The results indicate that China＇s futures market of commodity is a complicated nonlinear system with obvious nonlinear chaotic characteristic.展开更多
The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions. By combining neural...The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions. By combining neural networks and wavelet theories, the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given. Based on wavelet networks, a new method for parameter identification was suggested, which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series. Through pre-treatment and comparison of results before and after the treatment, several useful conclusions are reached: High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.展开更多
For a nonlinear power transmission system, the residue calculus method is introduced and applied to study its heteroclinic bifurcation. There a cone region and a strip region of parameters are obtained, in which the p...For a nonlinear power transmission system, the residue calculus method is introduced and applied to study its heteroclinic bifurcation. There a cone region and a strip region of parameters are obtained, in which the power transmission system displays chaotic oscillation. This gives a theoretic analysis and a computational method for the purpose to control the nonlinear system with deviation stably running.展开更多
Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a ...Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different kinds of chaotic data obtained from dynamical system has also been discussed in detail.展开更多
This paper reports a new three-dimensional autonomous chaotic system. It contains six control parameters and three nonlinear terms. Two cross-product terms are respectively in two equations. And one square term is in ...This paper reports a new three-dimensional autonomous chaotic system. It contains six control parameters and three nonlinear terms. Two cross-product terms are respectively in two equations. And one square term is in the third equation. Basic dynamic properties of the new system are investigated by means of theoretical analysis, numerical simulation, sensitivity to initial, power spectrum, Lyapunov exponent, and Poincar~ diagrams. The dynamic properties affected by variable parameters are also analysed. Finally, the chaotic system is simulated by circuit. The results verify the existence and implementation of the system.展开更多
Based on a coupled nonlinear dynamic filter （NDF）, a novel chaotic stream cipher is presented in this paper and employed to protect palmprint templates. The chaotic pseudorandom bit generator （PRBG） based on a cou...Based on a coupled nonlinear dynamic filter （NDF）, a novel chaotic stream cipher is presented in this paper and employed to protect palmprint templates. The chaotic pseudorandom bit generator （PRBG） based on a coupled NDF, which is constructed in an inverse flow, can generate multiple bits at one iteration and satisfy the security requirement of cipher design. Then, the stream cipher is employed to generate cancelable competitive code palmprint biometrics for template protection. The proposed cancelable palmprint authentication system depends on two factors： the palmprint biometric and the password/token. Therefore, the system provides high-confidence and also protects the user＇s privacy. The experimental results of verification on the Hong Kong PolyU Palmprint Database show that the proposed approach has a large template re-issuance ability and the equal error rate can achieve 0.02%. The performance of the palmprint template protection scheme proves the good practicability and security of the proposed stream cipher.展开更多
The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory. By using a designed nonlinear compensator mech...The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory. By using a designed nonlinear compensator mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example. From the Lyapunov stability theory, sufficient conditions for choosing control parameters to guarantee chaos control are derived. Several experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.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
文摘This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 60374037 and 60574036）, the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant 20050055013）, and the Program for New Century Excellent Talents of China （NCET）.
文摘A finite-time controller is designed for a class of nonlinear systems subject to sector nonlinear inputs. A novel and simple approach is suggested based on the finite-time control principle. The designed sliding-mode controller can drive a chaotic system to track a smooth target signal in a finite time. The chaotic Duffing-Holmes oscillator is used for verification and demonstration.
基金supported by the National Natural Science Foundation of China (Grant No.60704037)the Natural Science Foundation of Hebei Province,China (Grant No.F2010001317)the Doctor Foundation of Yanshan University of China (Grant No.B451)
文摘This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The. criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincare map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using nomfeedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to periodmotions by adding an excitation term.
基金Project supported by the Young Talents Natural Science Foundation for Universities of Anhui Province,China(Grant No.2012SQRL179)
文摘This paper presents a robust output feedback control method for uncertain chaotic systems, which comprises a nonlinear inversion-based controller with a fuzzy robust compensator. The proposed controller eliminates the unknown nonlinear function by using a fuzzy system, whose inputs are not the state variables but feedback error signals. The underlying stability analysis as well as parameter update law design are carried out by using the Lyapunov-based technique. The proposed method indicates that the nonlinear inversion-based control approach can also be applied to uncertain chaotic systems. Theoretical results are illustrated through two simulation examples.
基金supported by the National Natural Science Foundation of China(No.10632040)
文摘In this paper,determination of the characteristics of futures market in China is presented by the method of the phase-randomized surrogate data.There is a significant difference in the obtained critical values when this method is used for random timeseries and for nonlinear chaotic timeseries.The singular value decomposition is used to reduce noise in the chaotic timeseries.The phase space of chaotic timeseries is decomposed into range space and null noise space.The original chaotic timeseries in range space is restructured.The method of strong disturbance based on the improved general constrained randomized method is further adopted to re-deternination.With the calculated results,an analysis on the trend of futures market of commodity is made in this paper.The results indicate that China＇s futures market of commodity is a complicated nonlinear system with obvious nonlinear chaotic characteristic.
文摘The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions. By combining neural networks and wavelet theories, the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given. Based on wavelet networks, a new method for parameter identification was suggested, which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series. Through pre-treatment and comparison of results before and after the treatment, several useful conclusions are reached: High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.
文摘For a nonlinear power transmission system, the residue calculus method is introduced and applied to study its heteroclinic bifurcation. There a cone region and a strip region of parameters are obtained, in which the power transmission system displays chaotic oscillation. This gives a theoretic analysis and a computational method for the purpose to control the nonlinear system with deviation stably running.
基金The project supported by the National Natural Science Foundation of China(19672043)
文摘Certain deterministic nonlinear systems may show chaotic behavior. We consider the motion of qualitative information and the practicalities of extracting a part from chaotic experimental data. Our approach based on a theorem of Takens draws on the ideas from the generalized theory of information known as singular system analysis. We illustrate this technique by numerical data from the chaotic region of the chaotic experimental data. The method of the singular-value decomposition is used to calculate the eigenvalues of embedding space matrix. The corresponding concrete algorithm to calculate eigenvectors and to obtain the basis of embedding vector space is proposed in this paper. The projection on the orthogonal basis generated by eigenvectors of timeseries data and concrete paradigm are also provided here. Meanwhile the state space reconstruction technology of different kinds of chaotic data obtained from dynamical system has also been discussed in detail.
文摘This paper reports a new three-dimensional autonomous chaotic system. It contains six control parameters and three nonlinear terms. Two cross-product terms are respectively in two equations. And one square term is in the third equation. Basic dynamic properties of the new system are investigated by means of theoretical analysis, numerical simulation, sensitivity to initial, power spectrum, Lyapunov exponent, and Poincar~ diagrams. The dynamic properties affected by variable parameters are also analysed. Finally, the chaotic system is simulated by circuit. The results verify the existence and implementation of the system.
基金This work was partly supported by the National Natural Science Foundation of China （11501581）, the Project by Central South Uni- versity （502042032）, and the China Postdoctoral Science Foundation （2015M570683）.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60971104)the Basic Research Foundation of Sichuan Province,China (Grant No. 2006J013-011)+1 种基金the Outstanding Young Researchers Foundation of Sichuan Province,China (Grant No. 09ZQ026-091)the Research Fund for the Doctoral Program of Higher Education of China(Grant No. 20090184110008)
文摘Based on a coupled nonlinear dynamic filter （NDF）, a novel chaotic stream cipher is presented in this paper and employed to protect palmprint templates. The chaotic pseudorandom bit generator （PRBG） based on a coupled NDF, which is constructed in an inverse flow, can generate multiple bits at one iteration and satisfy the security requirement of cipher design. Then, the stream cipher is employed to generate cancelable competitive code palmprint biometrics for template protection. The proposed cancelable palmprint authentication system depends on two factors： the palmprint biometric and the password/token. Therefore, the system provides high-confidence and also protects the user＇s privacy. The experimental results of verification on the Hong Kong PolyU Palmprint Database show that the proposed approach has a large template re-issuance ability and the equal error rate can achieve 0.02%. The performance of the palmprint template protection scheme proves the good practicability and security of the proposed stream cipher.
基金Project supported by the National Natural Science Foundation of China (Grant No 50376029)
文摘The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory. By using a designed nonlinear compensator mechanism, the system deterministic nonlinearity, parametric uncertainty and disturbance effect can be compensated effectively. The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example. From the Lyapunov stability theory, sufficient conditions for choosing control parameters to guarantee chaos control are derived. Several experiments are carried out, including parameter change experiments, set-point change experiments and disturbance experiments. Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.
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.
