An approach is proposed to avoid model structure determination in system identification using NARMAX （nonlinear autoregressive moving average with exogenous inputs） model. Identification procedure is formulated as a...An approach is proposed to avoid model structure determination in system identification using NARMAX （nonlinear autoregressive moving average with exogenous inputs） model. Identification procedure is formulated as an optimization procedure of a apecial class of Hopfield network in the proposed approach. The particular structure of these Hopfield networks can avoid the local optimum problem. Training of these Hopfield network achieves model structure determination and parameter estimation. Convergence of Hopfield networks guarantees that a NARMAX model of random initial state will approach a valid identification model with accurate state parameters. Results of two simulation examples illustrate that this approach is efficient and simple.展开更多
This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectru...This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.展开更多
The nonseparable optimization control problem is considered, where the overall objective function is not of an additive form with respect to subsystems. Since there exists the problem that computation is very slow whe...The nonseparable optimization control problem is considered, where the overall objective function is not of an additive form with respect to subsystems. Since there exists the problem that computation is very slow when using iteratire algorithms in multiobjective optimization, Hopfield optimization hierarchical network based on IPM is presented to overcome such slow computation difficulty. Asymptotic stability of this Hopfield network is proved and its equilibrium point is the optimal point of the original problem. The simulation shows that the net is effective to deal with the optimization control problem for large-scale non.separable steady state systems.展开更多
The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations.We present the system in the glassy phase with low temperature and high memory load.We find that the inferenc...The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations.We present the system in the glassy phase with low temperature and high memory load.We find that the inference error is very sensitive to the form of state sampling.When a single state is sampled to compute magnetizations and correlations,the inference error is almost indistinguishable irrespective of the sampled state.However,the error can be greatly reduced if the data is collected with state transitions.Our result holds for different disorder samples and accounts for the previously observed large fluctuations of inference error at low temperatures.展开更多
This paper focuses on the issue of resilient dynamic output-feedback(DOF)control for H_∞synchronization of chaotic Hopfield networks with time-varying delay.The aim is to determine a DOF controller with gain perturba...This paper focuses on the issue of resilient dynamic output-feedback(DOF)control for H_∞synchronization of chaotic Hopfield networks with time-varying delay.The aim is to determine a DOF controller with gain perturbations ensuring that the H_∞norm from the external disturbances to the synchronization error is less than or equal to a prescribed bound.A delaydependent criterion for the H_∞synchronization is derived by employing the Lyapunov functional method together with some recent inequalities.Then,with the help of some decoupling techniques,sufficient conditions on the existence of the resilient DOF controller are developed for both the time-varying and constant time-delay cases.Lastly,an example is used to illustrate the applicability of the results obtained.展开更多
The paper is devoted to periodic attractor of delayed Hopfield neural networks with time-varying. By constructing Lyapunov functionals and using inequality techniques, some new sufficient criteria are obtained to guar...The paper is devoted to periodic attractor of delayed Hopfield neural networks with time-varying. By constructing Lyapunov functionals and using inequality techniques, some new sufficient criteria are obtained to guarantee the existence and global exponential stability of periodic attractor. Our results improve and extend some existing ones in [13-14]. One example is also worked out to demonstrate the advantages of our results.展开更多
The large-scale acquisition and widespread application of remote sensing image data have led to increasingly severe challenges in information security and privacy protection during transmission and storage.Urban remot...The large-scale acquisition and widespread application of remote sensing image data have led to increasingly severe challenges in information security and privacy protection during transmission and storage.Urban remote sensing image,characterized by complex content and well-defined structures,are particularly vulnerable to malicious attacks and information leakage.To address this issue,the author proposes an encryption method based on the enhanced single-neuron dynamical system(ESNDS).ESNDS generates highquality pseudo-random sequences with complex dynamics and intense sensitivity to initial conditions,which drive a structure of multi-stage cipher comprising permutation,ring-wise diffusion,and mask perturbation.Using representative GF-2 Panchromatic and Multispectral Scanner(PMS)urban scenes,the author conducts systematic evaluations in terms of inter-pixel correlation,information entropy,histogram uniformity,and number of pixel change rate(NPCR)/unified average changing intensity(UACI).The results demonstrate that the proposed scheme effectively resists statistical analysis,differential attacks,and known-plaintext attacks while maintaining competitive computational efficiency for high-resolution urban image.In addition,the cipher is lightweight and hardware-friendly,integrates readily with on-board and ground processing,and thus offers tangible engineering utility for real-time,large-volume remote-sensing data protection.展开更多
The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits.This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network(HNN)with coupled hyper...The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits.This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network(HNN)with coupled hyperbolic memristors through the modification of a single coupling connection weight.The bistable mode of the hyperbolic memristive HNN(mHNN),characterized by the coexistence of asymmetric chaos and periodic attractors,is effectively demonstrated through the utilization of conventional nonlinear analysis techniques.These techniques include bifurcation diagrams,two-parameter maximum Lyapunov exponent plots,local attractor basins,and phase trajectory diagrams.Moreover,an encryption technique for color images is devised by leveraging the mHNN model and asymmetric structural attractors.This method demonstrates significant benefits in correlation,information entropy,and resistance to differential attacks,providing strong evidence for its effectiveness in encryption.Additionally,an improved modular circuit design method is employed to create the analog equivalent circuit of the memristive HNN.The correctness of the circuit design is confirmed through Multisim simulations,which align with numerical simulations conducted in Matlab.展开更多
A method of generating multi-double scroll attractors is proposed based on the memristor Hopfield neural network(HNN)under pulse control.First,the original hyperbolic-type memristor is added to the neural network math...A method of generating multi-double scroll attractors is proposed based on the memristor Hopfield neural network(HNN)under pulse control.First,the original hyperbolic-type memristor is added to the neural network mathematical model,and the influence of this memristor on the dynamic behavior of the new HNN is analyzed.The numerical results show that after adding the memristor,the abundant dynamic behaviors such as chaos coexistence,period coexistence and chaos period coexistence can be observed when the initial value of the system is changed.Then the logic pulse is added to the external memristor.It is found that the equilibrium point of the HNN can multiply and generate multi-double scroll attractors after the pulse stimulation.When the number of logical pulses is changed,the number of multi-double scroll attractors will also change,so that the pulse can control the generation of multi-double scroll attractors.Finally,the HNN circuit under pulsed stimulation was realized by circuit simulation,and the results verified the correctness of the numerical results.展开更多
Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem and the counter...Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem and the counter proof method,and some sufficient conditions for the global asymptotic stability of the equilibrium point are obtained through the combination of a suitable Lyapunov function and an algebraic inequality technique.展开更多
本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Ra...本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Rassias稳定性的一个充分条件,从而提供了一种通过验证自反馈系数矩阵和权重系数矩阵判断神经网络具有Hyers-Ulam稳定性的方法.最后,本文设置满足定理的神经网络系数,利用仿真实验,验证此充分条件的正确性.展开更多
Hopfield neural network is a single layer feedforward neural network. Hopfield network requires some control parameters to be carefully selected, else the network is apt to converge to local minimum. An ant system is ...Hopfield neural network is a single layer feedforward neural network. Hopfield network requires some control parameters to be carefully selected, else the network is apt to converge to local minimum. An ant system is a nature inspired meta heuristic algorithm. It has been applied to several combinatorial optimization problems such as Traveling Salesman Problem, Scheduling Problems, etc. This paper will show an ant system may be used in tuning the network control parameters by a group of cooperated ants. The major advantage of this network is to adjust the network parameters automatically, avoiding a blind search for the set of control parameters. This network was tested on two TSP problems, 5 cities and 10 cities. The results have shown an obvious improvement.展开更多
This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay. Some Lyapunov-KrasoVskii functi...This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay. Some Lyapunov-KrasoVskii functionals are constructed and the linear matrix inequality （LMI） approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence, uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties. By using Leibniz-Newton formula, free weighting matrices are employed to express this relationship, which implies that the new criteria are less conservative than existing ones. Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.展开更多
This paper presents the finding of a novel chaotic system with one source and two saddle-foci in a simple three-dimensional （3D） autonomous continuous time Hopfield neural network. In particular, the system with one...This paper presents the finding of a novel chaotic system with one source and two saddle-foci in a simple three-dimensional （3D） autonomous continuous time Hopfield neural network. In particular, the system with one source and two saddle-foci has a chaotic attractor and a periodic attractor with different initial points, which has rarely been reported in 3D autonomous systems. The complex dynamical behaviours of the system are further investigated by means of a Lyapunov exponent spectrum, phase portraits and bifurcation analysis. By virtue of a result of horseshoe theory in dynamical systems, this paper presents rigorous computer-assisted verifications for the existence of a horseshoe in the system for a certain parameter.展开更多
This paper proposes new delay-dependent synchronization criteria for coupled Hopfield neural networks with time-varying delays. By construction of a suitable Lyapunov Krasovskii＇s functional and use of Finsler＇s lem...This paper proposes new delay-dependent synchronization criteria for coupled Hopfield neural networks with time-varying delays. By construction of a suitable Lyapunov Krasovskii＇s functional and use of Finsler＇s lemma, novel synchronization criteria for the networks are established in terms of linear matrix inequalities （LMIs） which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.展开更多
文摘An approach is proposed to avoid model structure determination in system identification using NARMAX （nonlinear autoregressive moving average with exogenous inputs） model. Identification procedure is formulated as an optimization procedure of a apecial class of Hopfield network in the proposed approach. The particular structure of these Hopfield networks can avoid the local optimum problem. Training of these Hopfield network achieves model structure determination and parameter estimation. Convergence of Hopfield networks guarantees that a NARMAX model of random initial state will approach a valid identification model with accurate state parameters. Results of two simulation examples illustrate that this approach is efficient and simple.
基金Project partially supported by the China Postdoctoral Science Foundation (Grant No. 20060400705)Tianjin University Research Foundation (Grant No. TJU-YFF-08B06)
文摘This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.
基金This project was supported by Postdoctoral Follows Foundation (2001)5 .
文摘The nonseparable optimization control problem is considered, where the overall objective function is not of an additive form with respect to subsystems. Since there exists the problem that computation is very slow when using iteratire algorithms in multiobjective optimization, Hopfield optimization hierarchical network based on IPM is presented to overcome such slow computation difficulty. Asymptotic stability of this Hopfield network is proved and its equilibrium point is the optimal point of the original problem. The simulation shows that the net is effective to deal with the optimization control problem for large-scale non.separable steady state systems.
基金Supported by the National Science Foundation of China under Grant Nos. 10774150,10834014the China 973-Program under Grant Nos. 2007CB935903 and HKUST605010
文摘The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations.We present the system in the glassy phase with low temperature and high memory load.We find that the inference error is very sensitive to the form of state sampling.When a single state is sampled to compute magnetizations and correlations,the inference error is almost indistinguishable irrespective of the sampled state.However,the error can be greatly reduced if the data is collected with state transitions.Our result holds for different disorder samples and accounts for the previously observed large fluctuations of inference error at low temperatures.
基金supported by the Natural Science Foundation of the Anhui Higher Education Institutions(Grant Nos.KJ2017A064 and KJ2018ZD007)the Excellent Youth Talent Support Program of Universities in Anhui Province(Grant No.GXYQZD2019021)the National Natural Science Foundation of China(Grant No.61503002).
文摘This paper focuses on the issue of resilient dynamic output-feedback(DOF)control for H_∞synchronization of chaotic Hopfield networks with time-varying delay.The aim is to determine a DOF controller with gain perturbations ensuring that the H_∞norm from the external disturbances to the synchronization error is less than or equal to a prescribed bound.A delaydependent criterion for the H_∞synchronization is derived by employing the Lyapunov functional method together with some recent inequalities.Then,with the help of some decoupling techniques,sufficient conditions on the existence of the resilient DOF controller are developed for both the time-varying and constant time-delay cases.Lastly,an example is used to illustrate the applicability of the results obtained.
基金Foundation item： Supported by the National Science Foundation of Hunan Provincial Education Department （06C792 07C700）
文摘The paper is devoted to periodic attractor of delayed Hopfield neural networks with time-varying. By constructing Lyapunov functionals and using inequality techniques, some new sufficient criteria are obtained to guarantee the existence and global exponential stability of periodic attractor. Our results improve and extend some existing ones in [13-14]. One example is also worked out to demonstrate the advantages of our results.
文摘The large-scale acquisition and widespread application of remote sensing image data have led to increasingly severe challenges in information security and privacy protection during transmission and storage.Urban remote sensing image,characterized by complex content and well-defined structures,are particularly vulnerable to malicious attacks and information leakage.To address this issue,the author proposes an encryption method based on the enhanced single-neuron dynamical system(ESNDS).ESNDS generates highquality pseudo-random sequences with complex dynamics and intense sensitivity to initial conditions,which drive a structure of multi-stage cipher comprising permutation,ring-wise diffusion,and mask perturbation.Using representative GF-2 Panchromatic and Multispectral Scanner(PMS)urban scenes,the author conducts systematic evaluations in terms of inter-pixel correlation,information entropy,histogram uniformity,and number of pixel change rate(NPCR)/unified average changing intensity(UACI).The results demonstrate that the proposed scheme effectively resists statistical analysis,differential attacks,and known-plaintext attacks while maintaining competitive computational efficiency for high-resolution urban image.In addition,the cipher is lightweight and hardware-friendly,integrates readily with on-board and ground processing,and thus offers tangible engineering utility for real-time,large-volume remote-sensing data protection.
基金Project supported by the National Nature Science Foundation of China(Grant Nos.51737003 and 51977060)the Natural Science Foundation of Hebei Province(Grant No.E2011202051).
文摘The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits.This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network(HNN)with coupled hyperbolic memristors through the modification of a single coupling connection weight.The bistable mode of the hyperbolic memristive HNN(mHNN),characterized by the coexistence of asymmetric chaos and periodic attractors,is effectively demonstrated through the utilization of conventional nonlinear analysis techniques.These techniques include bifurcation diagrams,two-parameter maximum Lyapunov exponent plots,local attractor basins,and phase trajectory diagrams.Moreover,an encryption technique for color images is devised by leveraging the mHNN model and asymmetric structural attractors.This method demonstrates significant benefits in correlation,information entropy,and resistance to differential attacks,providing strong evidence for its effectiveness in encryption.Additionally,an improved modular circuit design method is employed to create the analog equivalent circuit of the memristive HNN.The correctness of the circuit design is confirmed through Multisim simulations,which align with numerical simulations conducted in Matlab.
基金supported by the Guizhou Province Natural Science Foundation(Qiankehe Fundamentals-ZK[2023]General-055)Guizhou Province Science and Technology Support Plan Project(Qiankehe Fundamentals[2023]General-465)。
文摘A method of generating multi-double scroll attractors is proposed based on the memristor Hopfield neural network(HNN)under pulse control.First,the original hyperbolic-type memristor is added to the neural network mathematical model,and the influence of this memristor on the dynamic behavior of the new HNN is analyzed.The numerical results show that after adding the memristor,the abundant dynamic behaviors such as chaos coexistence,period coexistence and chaos period coexistence can be observed when the initial value of the system is changed.Then the logic pulse is added to the external memristor.It is found that the equilibrium point of the HNN can multiply and generate multi-double scroll attractors after the pulse stimulation.When the number of logical pulses is changed,the number of multi-double scroll attractors will also change,so that the pulse can control the generation of multi-double scroll attractors.Finally,the HNN circuit under pulsed stimulation was realized by circuit simulation,and the results verified the correctness of the numerical results.
基金Research supported by the National Natural Science Foundation of China(12271220)postgraduate research and practice innovation program of Jiangsu Province(KYCX24-3010)。
文摘Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem and the counter proof method,and some sufficient conditions for the global asymptotic stability of the equilibrium point are obtained through the combination of a suitable Lyapunov function and an algebraic inequality technique.
文摘本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Rassias稳定性的一个充分条件,从而提供了一种通过验证自反馈系数矩阵和权重系数矩阵判断神经网络具有Hyers-Ulam稳定性的方法.最后,本文设置满足定理的神经网络系数,利用仿真实验,验证此充分条件的正确性.
文摘Hopfield neural network is a single layer feedforward neural network. Hopfield network requires some control parameters to be carefully selected, else the network is apt to converge to local minimum. An ant system is a nature inspired meta heuristic algorithm. It has been applied to several combinatorial optimization problems such as Traveling Salesman Problem, Scheduling Problems, etc. This paper will show an ant system may be used in tuning the network control parameters by a group of cooperated ants. The major advantage of this network is to adjust the network parameters automatically, avoiding a blind search for the set of control parameters. This network was tested on two TSP problems, 5 cities and 10 cities. The results have shown an obvious improvement.
基金This work is supported by the National Natural Science Foundation of China (No.60674026)the Key Research Foundation of Science and Technology of the Ministry of Education of China (No.107058).
文摘This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay. Some Lyapunov-KrasoVskii functionals are constructed and the linear matrix inequality （LMI） approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence, uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties. By using Leibniz-Newton formula, free weighting matrices are employed to express this relationship, which implies that the new criteria are less conservative than existing ones. Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.
基金Project supported by the National Natural Science Foundation of China(Grant No.60774088)the Program for New Century Excellent Talents in University of China(NCET)+1 种基金the Science & Technology Research Key Project of Educational Ministry of China(Grant No.107024)the Foundation of the Application Base and Frontier Technology Research Project of Tianjin(Grant No.08JCZDJC21900)
文摘This paper presents the finding of a novel chaotic system with one source and two saddle-foci in a simple three-dimensional （3D） autonomous continuous time Hopfield neural network. In particular, the system with one source and two saddle-foci has a chaotic attractor and a periodic attractor with different initial points, which has rarely been reported in 3D autonomous systems. The complex dynamical behaviours of the system are further investigated by means of a Lyapunov exponent spectrum, phase portraits and bifurcation analysis. By virtue of a result of horseshoe theory in dynamical systems, this paper presents rigorous computer-assisted verifications for the existence of a horseshoe in the system for a certain parameter.
基金supported by the Basic Science Research Program Through the National Research Foundation of Korea(NRF) Funded by the Ministry of Education,Science and Technology(Grant Nos.2011-0001045 and 2011-0009273)
文摘This paper proposes new delay-dependent synchronization criteria for coupled Hopfield neural networks with time-varying delays. By construction of a suitable Lyapunov Krasovskii＇s functional and use of Finsler＇s lemma, novel synchronization criteria for the networks are established in terms of linear matrix inequalities （LMIs） which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.
