We show that chaotic state can be produced as an output of vacuum state evolving in diffusion channel,while displaced chaotic state is output of a coherent state evolving in diffusion channel.We also introduce the the...We show that chaotic state can be produced as an output of vacuum state evolving in diffusion channel,while displaced chaotic state is output of a coherent state evolving in diffusion channel.We also introduce the thermo vaccum state for the displaced chaotic state and evaluate the average photon number.The displaced chaotic state may be used exhibiting quantum controlling.展开更多
A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach ...A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features：（i） it enables synchronization to be achieved for both cases of n 〈 m and n 〉 m;（ii） it is rigorous,being based on theorems;（iii） it can be readily applied to any chaotic（hyperchaotic） maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map（as the drive system） and the three-dimensional hyperchaotic Wang map（as the response system）,and the three-dimensional H′enon-like map（as the drive system） and the two-dimensional Lorenz discrete-time system（as the response system）.展开更多
A state-observer based full-state asymptotic trajectory control （OFSTC） method requiring a scalar state is presented to asymptotically drive all the states of chaotic systems to arbitrary desired trajectories. It is...A state-observer based full-state asymptotic trajectory control （OFSTC） method requiring a scalar state is presented to asymptotically drive all the states of chaotic systems to arbitrary desired trajectories. It is no surprise that OFSTC can obtain good tracking performance as desired due to using a state-observer. Significantly OFSTC requires only a scalar state of chaotic systems. A sinusoidal wave and two chaotic variables were taken as illustrative tracking trajectories to validate that using OFSTC can make all the states of a unified chaotic system track the desired trajectories with high tracking accuracy and in a finite time. It is noted that this is the first time that the state-observer of chaotic systems is designed on the basis of Kharitonov＇s Theorem.展开更多
We investigate how an optical squeezed chaotic field（SCF） evolves in an amplitude dissipation channel. We have used the integration within ordered product of operators technique to derive its evolution law. We also ...We investigate how an optical squeezed chaotic field（SCF） evolves in an amplitude dissipation channel. We have used the integration within ordered product of operators technique to derive its evolution law. We also show that the density operator of SCF can be viewed as a generating field of the squeezed number state.展开更多
A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable ...A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable and its （q-order and 2q-order） time derivatives. This idea is demonstrated by using several well-known fractional-order chaotic systems. Finally, a synchronization scheme is investigated for this fractional-order chaotic system via a specific state variable and its （q-order and 2q-order） time derivatives. Some examples are used to illustrate the effectiveness of the proposed synchronization method.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
For the density operator（mixed state） describing squeezed chaotic light（SCL） we search for its thermal vacuum state（a pure state） in the real-fictitious space. Using the method of integration within ordered prod...For the density operator（mixed state） describing squeezed chaotic light（SCL） we search for its thermal vacuum state（a pure state） in the real-fictitious space. Using the method of integration within ordered product（IWOP） of operators we find that it is a kind of one- and two-mode combinatorial squeezed state. Its application in evaluating the quantum fluctuation of photon number reveals： the stronger the squeezing is, the larger a fluctuation appears. The second-order degree of coherence of SCL is also deduced which shows that SCL is classic. The new thermal vacuum state also helps to derive the Wigner function of SCL.展开更多
An effective power quality prediction for regional power grid can provide valuable references and contribute to the discovering and solving of power quality problems. So a predicting model for power quality steady sta...An effective power quality prediction for regional power grid can provide valuable references and contribute to the discovering and solving of power quality problems. So a predicting model for power quality steady state index based on chaotic theory and least squares support vector machine (LSSVM) is proposed in this paper. At first, the phase space reconstruction of original power quality data is performed to form a new data space containing the attractor. The new data space is used as training samples for the LSSVM. Then in order to predict power quality steady state index accurately, the particle swarm algorithm is adopted to optimize parameters of the LSSVM model. According to the simulation results based on power quality data measured in a certain distribution network, the model applies to several indexes with higher forecasting accuracy and strong practicability.展开更多
In this paper we present a new projective synchronization scheme, where two chaotic （hyperchaotic） discrete-time systems synchronize for any arbitrary scaling matrix. Specifically, each drive system state synchroniz...In this paper we present a new projective synchronization scheme, where two chaotic （hyperchaotic） discrete-time systems synchronize for any arbitrary scaling matrix. Specifically, each drive system state synchronizes with a linear combination of response system states. The proposed observer-based approach presents some useful features： i） it enables exact synchronization to be achieved in finite time （i.e., dead-beat synchronization）; ii） it exploits a scalar synchronizing signal; iii） it can be applied to a wide class of discrete-time chaotic （hyperchaotic） systems; iv） it includes, as a particular case, most of the synchronization types defined so far. An example is reported, which shows in detail that exact synchronization is effectively achieved in finite time, using a scalar synchronizing signal only, for any arbitrary scaling matrix.展开更多
The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state＇s evolution during the diffusion process, fully utiliz...The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state＇s evolution during the diffusion process, fully utilizing the technique of integration within an ordered product （IWOP） of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dp/dt = -κ[a＋ap -a＋pa -apa＋ ＋ paa＋]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.展开更多
Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously...Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.展开更多
The PC synchronization of a class of chaotic systems is investigated in this paper. The drive system is assumed to have only one state variable available. By constructing proper observers, some novel criteria for PC s...The PC synchronization of a class of chaotic systems is investigated in this paper. The drive system is assumed to have only one state variable available. By constructing proper observers, some novel criteria for PC synchronization are proposed via event-triggered control scheme. The Lii system and Chen system are taken as examples to demonstrate the efficiency of the proposed approach.展开更多
This paper first investigates the observer of a class of chaotic systems, and then discusses the synchronization between two identical Hindmarsh–Rose（HR） neuronal chaotic systems. Both the drive and response system...This paper first investigates the observer of a class of chaotic systems, and then discusses the synchronization between two identical Hindmarsh–Rose（HR） neuronal chaotic systems. Both the drive and response systems are assumed to have only one state variable available. By constructing proper observers, some novel criteria for synchronization are proposed via a scalar input. Numerical simulations are given to demonstrate the efficiency of the proposed approach.展开更多
This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition ...This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.展开更多
This paper applies both the neural network and adaptive neuro-fuzzy inference system for forecasting short-term chaotic traffic volumes and compares the results. The architecture of the neural network consists of the ...This paper applies both the neural network and adaptive neuro-fuzzy inference system for forecasting short-term chaotic traffic volumes and compares the results. The architecture of the neural network consists of the input vector, one hidden layer and output layer. Bayesian regularization is employed to obtain the effective number of neurons in the hidden layer. The input variables and target of the adaptive neuro-fuzzy inference system are the same as those of the neural network. The data clustering technique is used to group data points so that the membership functions will be more tailored to the input data, which in turn greatly reduces the number of fuzzy rules. Numerical results indicate that these two models have almost the same accuracy, while the adaptive neuro-fuzzy inference system takes more time to train. It is also shown that although the effective number of neurons in the hidden layer is less than half the number of the input elements, the neural network can have satisfactory performance.展开更多
In this paper, a method is introduced to construct controller for the synchronization between two fractional order Rossler systems. The key thought is converting a fractional order system into an integer system. The c...In this paper, a method is introduced to construct controller for the synchronization between two fractional order Rossler systems. The key thought is converting a fractional order system into an integer system. The controller uses general linear state error feedback scheme. Numerical examples are given to demonstrate the effectiveness of the proposed method.展开更多
基金Project supported by the Natural Science Fund of the Education Department of Anhui Province,China(Grant No.KJ2016A590)the Talent Foundation of Hefei University,China(Grant No.15RC11)+2 种基金the Science Fund of Hefei University,China(Grant No.2016dtr02)the Talent Development Funding of Hefei University,China(Grant No.18-19RC60)the National Natural Science Foundation of China(Grant No.11804074)。
文摘We show that chaotic state can be produced as an output of vacuum state evolving in diffusion channel,while displaced chaotic state is output of a coherent state evolving in diffusion channel.We also introduce the thermo vaccum state for the displaced chaotic state and evaluate the average photon number.The displaced chaotic state may be used exhibiting quantum controlling.
文摘A new synchronization scheme for chaotic（hyperchaotic） maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features：（i） it enables synchronization to be achieved for both cases of n 〈 m and n 〉 m;（ii） it is rigorous,being based on theorems;（iii） it can be readily applied to any chaotic（hyperchaotic） maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map（as the drive system） and the three-dimensional hyperchaotic Wang map（as the response system）,and the three-dimensional H′enon-like map（as the drive system） and the two-dimensional Lorenz discrete-time system（as the response system）.
文摘A state-observer based full-state asymptotic trajectory control （OFSTC） method requiring a scalar state is presented to asymptotically drive all the states of chaotic systems to arbitrary desired trajectories. It is no surprise that OFSTC can obtain good tracking performance as desired due to using a state-observer. Significantly OFSTC requires only a scalar state of chaotic systems. A sinusoidal wave and two chaotic variables were taken as illustrative tracking trajectories to validate that using OFSTC can make all the states of a unified chaotic system track the desired trajectories with high tracking accuracy and in a finite time. It is noted that this is the first time that the state-observer of chaotic systems is designed on the basis of Kharitonov＇s Theorem.
基金Project supported by the National Natural Science Foundation of China(Grant No.10574647)the Natural Science Foundation of Shandong Province,China(Grant No.Y2008A16)the University Experimental Technology Foundation of Shandong Province of China(Grant No.S04W138)
文摘We investigate how an optical squeezed chaotic field（SCF） evolves in an amplitude dissipation channel. We have used the integration within ordered product of operators technique to derive its evolution law. We also show that the density operator of SCF can be viewed as a generating field of the squeezed number state.
文摘A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable and its （q-order and 2q-order） time derivatives. This idea is demonstrated by using several well-known fractional-order chaotic systems. Finally, a synchronization scheme is investigated for this fractional-order chaotic system via a specific state variable and its （q-order and 2q-order） time derivatives. Some examples are used to illustrate the effectiveness of the proposed synchronization method.
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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.1117511311447202and 11574295)
文摘For the density operator（mixed state） describing squeezed chaotic light（SCL） we search for its thermal vacuum state（a pure state） in the real-fictitious space. Using the method of integration within ordered product（IWOP） of operators we find that it is a kind of one- and two-mode combinatorial squeezed state. Its application in evaluating the quantum fluctuation of photon number reveals： the stronger the squeezing is, the larger a fluctuation appears. The second-order degree of coherence of SCL is also deduced which shows that SCL is classic. The new thermal vacuum state also helps to derive the Wigner function of SCL.
文摘An effective power quality prediction for regional power grid can provide valuable references and contribute to the discovering and solving of power quality problems. So a predicting model for power quality steady state index based on chaotic theory and least squares support vector machine (LSSVM) is proposed in this paper. At first, the phase space reconstruction of original power quality data is performed to form a new data space containing the attractor. The new data space is used as training samples for the LSSVM. Then in order to predict power quality steady state index accurately, the particle swarm algorithm is adopted to optimize parameters of the LSSVM model. According to the simulation results based on power quality data measured in a certain distribution network, the model applies to several indexes with higher forecasting accuracy and strong practicability.
文摘In this paper we present a new projective synchronization scheme, where two chaotic （hyperchaotic） discrete-time systems synchronize for any arbitrary scaling matrix. Specifically, each drive system state synchronizes with a linear combination of response system states. The proposed observer-based approach presents some useful features： i） it enables exact synchronization to be achieved in finite time （i.e., dead-beat synchronization）; ii） it exploits a scalar synchronizing signal; iii） it can be applied to a wide class of discrete-time chaotic （hyperchaotic） systems; iv） it includes, as a particular case, most of the synchronization types defined so far. An example is reported, which shows in detail that exact synchronization is effectively achieved in finite time, using a scalar synchronizing signal only, for any arbitrary scaling matrix.
基金Project supported by the National Basic Research Program of China(Grant No.2012CB922103)the National Natural Science Foundation of China(GrantNos.11175113 and 11274104)the Natural Science Foundation of Hubei Province of China(Grant No.2011CDA021)
文摘The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state＇s evolution during the diffusion process, fully utilizing the technique of integration within an ordered product （IWOP） of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dp/dt = -κ[a＋ap -a＋pa -apa＋ ＋ paa＋]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.
文摘Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.
基金supported by the National Natural Science Foundation of China(Grant Nos.11361043 and 61304161)the Natural Science Foundation of Jiangxi Province,China(Grant No.20122BAB201005)
文摘The PC synchronization of a class of chaotic systems is investigated in this paper. The drive system is assumed to have only one state variable available. By constructing proper observers, some novel criteria for PC synchronization are proposed via event-triggered control scheme. The Lii system and Chen system are taken as examples to demonstrate the efficiency of the proposed approach.
基金supported by the National Natural Science Foundation of China(Grant Nos.11361043 and 61304161)the Natural Science Foundation of Jiangxi Province,China(Grant No.20122BAB201005)the Scientific and Technological Project Foundation of Jiangxi Province Education Office,China(Grant No.GJJ14156)
文摘This paper first investigates the observer of a class of chaotic systems, and then discusses the synchronization between two identical Hindmarsh–Rose（HR） neuronal chaotic systems. Both the drive and response systems are assumed to have only one state variable available. By constructing proper observers, some novel criteria for synchronization are proposed via a scalar input. Numerical simulations are given to demonstrate the efficiency of the proposed approach.
基金supported by the National Natural Science Foundation of China (Grant No. 60702023)Natural Science Foundation of Zhejiang Province (Grant No. Y107440)
文摘This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the equivalent passivity＇＇ method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.
文摘This paper applies both the neural network and adaptive neuro-fuzzy inference system for forecasting short-term chaotic traffic volumes and compares the results. The architecture of the neural network consists of the input vector, one hidden layer and output layer. Bayesian regularization is employed to obtain the effective number of neurons in the hidden layer. The input variables and target of the adaptive neuro-fuzzy inference system are the same as those of the neural network. The data clustering technique is used to group data points so that the membership functions will be more tailored to the input data, which in turn greatly reduces the number of fuzzy rules. Numerical results indicate that these two models have almost the same accuracy, while the adaptive neuro-fuzzy inference system takes more time to train. It is also shown that although the effective number of neurons in the hidden layer is less than half the number of the input elements, the neural network can have satisfactory performance.
基金the Key Science Research Project of Southwest University for Nationalities under Grant No. 234778.
文摘In this paper, a method is introduced to construct controller for the synchronization between two fractional order Rossler systems. The key thought is converting a fractional order system into an integer system. The controller uses general linear state error feedback scheme. Numerical examples are given to demonstrate the effectiveness of the proposed method.
