The functionality of the biological brain is closely related to the dynamic behavior generated by synapses in its complex neural system.The self-connection synapse,as a critical form of feedback synapse in Hopfield ne...The functionality of the biological brain is closely related to the dynamic behavior generated by synapses in its complex neural system.The self-connection synapse,as a critical form of feedback synapse in Hopfield neurons,plays an essential role in understanding the dynamic behavior of the brain.Synaptic memristors can bring neural network models closer to the complexity of the brain's neural networks.Inspired by this,this study incorporates the nonlinear memory characteristics of synapses into the Hopfield neural network(HNN)by replacing a single self-synapse in a four-dimensional HNN model with a novel cosine memristor model,aiming to more realistically reproduce the dynamical behavior of biological neurons in artificial systems.By performing a dynamical analysis of the system using numerical methods,we find that the model exhibits infinitely many equilibrium points and can induce the formation of rare transient attractors,as well as an arbitrary number of multi-scroll attractors.Additionally,the model demonstrates complex coexisting attractor dynamics,including transient chaos,periodicity,decaying periodicity,and coexisting chaos.Furthermore,the feasibility of the proposed HNN model is verified using a field-programmable gate array(FPGA).Finally,an electronic codebook(ECB)–mode block cipher encryption algorithm is proposed for image encryption.The encryption performance is evaluated,with an information entropy value of 7.9993,demonstrating the excellent randomness of the system-generated numbers.展开更多
Neural synchronization is associated with various brain disorders,making it essential to investigate the intrinsic factors that influence the synchronization of coupled neural networks.In this paper,we propose a minim...Neural synchronization is associated with various brain disorders,making it essential to investigate the intrinsic factors that influence the synchronization of coupled neural networks.In this paper,we propose a minimal architecture as a prototype,consisting of two bi-neuron Hopfield neural networks(HNNs)coupled via a memristor.This coupling elevates the original two bi-neuron HNNs into a five-dimensional system,featuring an unstable line equilibrium set and rich dynamics absent in the uncoupled case.Our results show that varying the coupling strength and the initial state of the memristor can induce periodic,chaotic,hyperchaotic,and quasi-periodic oscillations,as well as initial-offset-regulated multistability.We derive sufficient conditions for achieving exponential synchronization and identify multiple synchronous regimes with transitions that strongly depend on the initial states.Field-programmable gate array(FPGA)implementation confirms the predicted dynamics and synchronization in real time,demonstrating that the memristive coupler enables complex dynamics and controllable synchronization in the most compact Hopfield architecture,with implications for the study of neuromorphic circuits and synchronization.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
By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural ...By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.展开更多
Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network.As it is well known,the stability of neural networks is not only the most basic and important problem but also foundation...Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network.As it is well known,the stability of neural networks is not only the most basic and important problem but also foundation of the network's applications.The stability of discrete HJopfield neural networks with delay is mainly investigated by using Lyapunov function.The sufficient conditions for the networks with delay converging towards a limit cycle of length 4 are obtained.Also,some sufficient criteria are given to ensure the networks having neither a stable state nor a limit cycle with length 2.The obtained results here generalize the previous results on stability of discrete Hopfield neural network with delay and without delay.展开更多
A new product conceptual design approach is put forward based on Hopfield neural networks models. By research on the mechanisms of Hopfield neural networks, the associative simulation approaches are proposed. The appr...A new product conceptual design approach is put forward based on Hopfield neural networks models. By research on the mechanisms of Hopfield neural networks, the associative simulation approaches are proposed. The approach is given by Hebb learn- ing law, Hopfield neural networks and crossover and mutation. The calculating models and the calculating formulas for the concep- tual design are put forward. Finally, an example for the conceptual design of a solar energy lamp is given. The better results are ob- tained in the conceptual design.展开更多
Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neur...Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.展开更多
In this study, a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional. This ...In this study, a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional. This paper presents the comprehensive discussion of the approach and also extensive applications.展开更多
The global stability problem of Takagi-Sugeno（T-S） fuzzy Hopfield neural networks（FHNNs） with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guar...The global stability problem of Takagi-Sugeno（T-S） fuzzy Hopfield neural networks（FHNNs） with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler＇s lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.展开更多
A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) + WIf(t,u(t)) + WIτf7τ(uτ(t)] dt +σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studie...A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) + WIf(t,u(t)) + WIτf7τ(uτ(t)] dt +σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.展开更多
The algorithm of Hopfield neural network filtering and estimation is studied. The model of vehicular dead reckoning system fitting for the algorithm is constructed, and the design scheme of system filtering and estima...The algorithm of Hopfield neural network filtering and estimation is studied. The model of vehicular dead reckoning system fitting for the algorithm is constructed, and the design scheme of system filtering and estimation based on Hopfield network is proposed. Compared with Kalman filter, the algorithm does not require very precise system model and the prior knowledge of noise statistics and does not diverge easily. The simulation results show that the vehicular dead reckoning system based on Hopfield network filtering and estimation has the good position precision, and needn't require the inertial sensors with high precision. Therefore, the algorithm has the good practicability.展开更多
This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel d...This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel delay-dependent condition is established to guarantee the existence and global asymptotic stability of the unique equilibrium point for a given delayed Hopfield neural network. This criterion is expressed in terms of linear matrix inequalities （LMIs）, which can be easily checked by utilizing the recently developed algorithms for solving LMIs. Examples are provided to demonstrate the effectiveness and reduced conservatism of the proposed condition.展开更多
In this note, we would like to point out that （i） of Corollary 1 given by Zhang et al. （cf Commun. Theor. Phys. 39 （2003） 381） is incorrect in general.
The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stabilit...The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found. The result obtained holds not only for constant delay but also for time-varying delays.展开更多
A memristive Hopfield neural network(MHNN)with a special activation gradient is proposed by adding a suitable memristor to the Hopfield neural network(HNN)with a special activation gradient.The MHNN is simulated and d...A memristive Hopfield neural network(MHNN)with a special activation gradient is proposed by adding a suitable memristor to the Hopfield neural network(HNN)with a special activation gradient.The MHNN is simulated and dynamically analyzed,and implemented on FPGA.Then,a new pseudo-random number generator(PRNG)based on MHNN is proposed.The post-processing unit of the PRNG is composed of nonlinear post-processor and XOR calculator,which effectively ensures the randomness of PRNG.The experiments in this paper comply with the IEEE 754-1985 high precision32-bit floating point standard and are done on the Vivado design tool using a Xilinx XC7 Z020 CLG400-2 FPGA chip and the Verilog-HDL hardware programming language.The random sequence generated by the PRNG proposed in this paper has passed the NIST SP800-22 test suite and security analysis,proving its randomness and high performance.Finally,an image encryption system based on PRNG is proposed and implemented on FPGA,which proves the value of the image encryption system in the field of data encryption connected to the Internet of Things(Io T).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
Hopfield neural networks on scale-free networks display the power law relation between the stability of patterns and the number of patterns.The stability is measured by the overlap between the output state and the sto...Hopfield neural networks on scale-free networks display the power law relation between the stability of patterns and the number of patterns.The stability is measured by the overlap between the output state and the stored pattern which is presented to a neural network.In simulations the overlap declines to a constant by a power law decay.Here we provide the explanation for the power law behavior through the signal-to-noise ratio analysis.We show that on sparse networks storing a plenty of patterns the stability of stored patterns can be approached by a power law function with the exponent-0.5.There is a difference between analytic and simulation results that the analytic results of overlap decay to 0.The difference exists because the signal and noise term of nodes diverge from the mean-field approach in the sparse finite size networks.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
基金supported by the Guiding Science and Technology Plan Project of Changsha City under Grant kzd2501129by the Natural Science Foundation of Hunan Province(Grant No.2025JJ50368)+1 种基金the Scientific Research Fund of Hunan Provincial Education Department(Grant No.24A0248)the National Natural Science Foundation of China(Grant No.62273141)。
文摘The functionality of the biological brain is closely related to the dynamic behavior generated by synapses in its complex neural system.The self-connection synapse,as a critical form of feedback synapse in Hopfield neurons,plays an essential role in understanding the dynamic behavior of the brain.Synaptic memristors can bring neural network models closer to the complexity of the brain's neural networks.Inspired by this,this study incorporates the nonlinear memory characteristics of synapses into the Hopfield neural network(HNN)by replacing a single self-synapse in a four-dimensional HNN model with a novel cosine memristor model,aiming to more realistically reproduce the dynamical behavior of biological neurons in artificial systems.By performing a dynamical analysis of the system using numerical methods,we find that the model exhibits infinitely many equilibrium points and can induce the formation of rare transient attractors,as well as an arbitrary number of multi-scroll attractors.Additionally,the model demonstrates complex coexisting attractor dynamics,including transient chaos,periodicity,decaying periodicity,and coexisting chaos.Furthermore,the feasibility of the proposed HNN model is verified using a field-programmable gate array(FPGA).Finally,an electronic codebook(ECB)–mode block cipher encryption algorithm is proposed for image encryption.The encryption performance is evaluated,with an information entropy value of 7.9993,demonstrating the excellent randomness of the system-generated numbers.
基金supported by the National Natural Science Foundation of China(Grant No.62271088)the Qinglan Project of Jiangsu Province+2 种基金the Jiangsu Government Scholarship for Overseas Studiesthe Training Plan of Young Backbone Teachers in Universities of Henan Province(Grant No.2023GGJS142)the Key Scientific Research of Colleges and Universities in Henan Province(Grant No.25A120009)。
文摘Neural synchronization is associated with various brain disorders,making it essential to investigate the intrinsic factors that influence the synchronization of coupled neural networks.In this paper,we propose a minimal architecture as a prototype,consisting of two bi-neuron Hopfield neural networks(HNNs)coupled via a memristor.This coupling elevates the original two bi-neuron HNNs into a five-dimensional system,featuring an unstable line equilibrium set and rich dynamics absent in the uncoupled case.Our results show that varying the coupling strength and the initial state of the memristor can induce periodic,chaotic,hyperchaotic,and quasi-periodic oscillations,as well as initial-offset-regulated multistability.We derive sufficient conditions for achieving exponential synchronization and identify multiple synchronous regimes with transitions that strongly depend on the initial states.Field-programmable gate array(FPGA)implementation confirms the predicted dynamics and synchronization in real time,demonstrating that the memristive coupler enables complex dynamics and controllable synchronization in the most compact Hopfield architecture,with implications for the study of neuromorphic circuits and synchronization.
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.
基金The Soft Project (B30145) of Science and Technology of Hunan Province.
文摘By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.
基金supported by China Postdoctoral Science Foundation(2003033516)partly supported by Open Founda-tion of University Key Lab of Information Sciences and Engineering,Dalian University,
文摘Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network.As it is well known,the stability of neural networks is not only the most basic and important problem but also foundation of the network's applications.The stability of discrete HJopfield neural networks with delay is mainly investigated by using Lyapunov function.The sufficient conditions for the networks with delay converging towards a limit cycle of length 4 are obtained.Also,some sufficient criteria are given to ensure the networks having neither a stable state nor a limit cycle with length 2.The obtained results here generalize the previous results on stability of discrete Hopfield neural network with delay and without delay.
基金Partially Supported by National Natural Science Foundation of China(No.50975033,No.60875046)Education Office of Liaoning Province(No.LR2013060)Natural Science Foundation of Liaoning Province(No.2013020123)
文摘A new product conceptual design approach is put forward based on Hopfield neural networks models. By research on the mechanisms of Hopfield neural networks, the associative simulation approaches are proposed. The approach is given by Hebb learn- ing law, Hopfield neural networks and crossover and mutation. The calculating models and the calculating formulas for the concep- tual design are put forward. Finally, an example for the conceptual design of a solar energy lamp is given. The better results are ob- tained in the conceptual design.
文摘Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.
基金Project supported by the National Natural Science Foundations of China (Grant Nos. 70571030 and 90610031)the Society Science Foundation from Ministry of Education of China (Grant No. 08JA790057)the Advanced Talents’ Foundation and Student’s Foundation of Jiangsu University (Grant Nos. 07JDG054 and 07A075)
文摘In this study, a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional. This paper presents the comprehensive discussion of the approach and also extensive applications.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60974004)the Natural Science Foundation of Jilin Province,China (Grant No. 201115222)
文摘The global stability problem of Takagi-Sugeno（T-S） fuzzy Hopfield neural networks（FHNNs） with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler＇s lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.
基金This project was supported by the National Natural Science Foundation of China (60074008, 60274007, 60274026) National Doctor foundaction of China (20010487005).
文摘A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) + WIf(t,u(t)) + WIτf7τ(uτ(t)] dt +σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.
文摘The algorithm of Hopfield neural network filtering and estimation is studied. The model of vehicular dead reckoning system fitting for the algorithm is constructed, and the design scheme of system filtering and estimation based on Hopfield network is proposed. Compared with Kalman filter, the algorithm does not require very precise system model and the prior knowledge of noise statistics and does not diverge easily. The simulation results show that the vehicular dead reckoning system based on Hopfield network filtering and estimation has the good position precision, and needn't require the inertial sensors with high precision. Therefore, the algorithm has the good practicability.
基金supported by National Natural Science Foundation of China (No. 60674027, 60875039, 60904022 and 60974127)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050446001)+2 种基金China Postdoctoral Science Foundation(No. 20070410336)Postdoctoral Foundation of Jiangsu Province(No. 0602042B)Scientific Research Foundation of Qufu Normal University
文摘This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel delay-dependent condition is established to guarantee the existence and global asymptotic stability of the unique equilibrium point for a given delayed Hopfield neural network. This criterion is expressed in terms of linear matrix inequalities （LMIs）, which can be easily checked by utilizing the recently developed algorithms for solving LMIs. Examples are provided to demonstrate the effectiveness and reduced conservatism of the proposed condition.
文摘In this note, we would like to point out that （i） of Corollary 1 given by Zhang et al. （cf Commun. Theor. Phys. 39 （2003） 381） is incorrect in general.
基金Project supported by the Program for New Century Excellent Talents in University (Grant No NCET-06-0298)the Program for Liaoning Excellent Talents in University (Grant No RC-05-07)+1 种基金the Program for Study of Science of the Educational Department of Liaoning Province, China (Grant No 05L020)the Program for Dalian Science and Technology of China (Grant No2005A10GX106)
文摘The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found. The result obtained holds not only for constant delay but also for time-varying delays.
基金supported by the Scientific Research Fund of Hunan Provincial Education Department(Grant No.21B0345)the Postgraduate Scientific Research Innovation Project of Changsha University of Science and Technology(Grant Nos.CX2021SS69 and CX2021SS72)+3 种基金the Postgraduate Scientific Research Innovation Project of Hunan Province,China(Grant No.CX20200884)the Natural Science Foundation of Hunan Province,China(Grant Nos.2019JJ50648,2020JJ4622,and 2020JJ4221)the National Natural Science Foundation of China(Grant No.62172058)the Special Funds for the Construction of Innovative Provinces of Hunan Province,China(Grant Nos.2020JK4046 and 2022SK2007)。
文摘A memristive Hopfield neural network(MHNN)with a special activation gradient is proposed by adding a suitable memristor to the Hopfield neural network(HNN)with a special activation gradient.The MHNN is simulated and dynamically analyzed,and implemented on FPGA.Then,a new pseudo-random number generator(PRNG)based on MHNN is proposed.The post-processing unit of the PRNG is composed of nonlinear post-processor and XOR calculator,which effectively ensures the randomness of PRNG.The experiments in this paper comply with the IEEE 754-1985 high precision32-bit floating point standard and are done on the Vivado design tool using a Xilinx XC7 Z020 CLG400-2 FPGA chip and the Verilog-HDL hardware programming language.The random sequence generated by the PRNG proposed in this paper has passed the NIST SP800-22 test suite and security analysis,proving its randomness and high performance.Finally,an image encryption system based on PRNG is proposed and implemented on FPGA,which proves the value of the image encryption system in the field of data encryption connected to the Internet of Things(Io T).
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This work was supported by NSFC(Grant No.11675096)FPALAB-SNNU(Grant No.16QNGG007).
文摘Hopfield neural networks on scale-free networks display the power law relation between the stability of patterns and the number of patterns.The stability is measured by the overlap between the output state and the stored pattern which is presented to a neural network.In simulations the overlap declines to a constant by a power law decay.Here we provide the explanation for the power law behavior through the signal-to-noise ratio analysis.We show that on sparse networks storing a plenty of patterns the stability of stored patterns can be approached by a power law function with the exponent-0.5.There is a difference between analytic and simulation results that the analytic results of overlap decay to 0.The difference exists because the signal and noise term of nodes diverge from the mean-field approach in the sparse finite size networks.
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.
