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
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
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
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
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
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 foundati...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
The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differen...The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium （if it exists） is globally asymptotically stable and this implies that the equilibrium of the system is unique.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
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.
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.
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.
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.
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.
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Project supported by the National Natural Science Foundation of China (No.10571078)the Natural Science Foundation of Gansu Province of China (No.3ZX062-B25-012)
文摘The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium （if it exists） is globally asymptotically stable and this implies that the equilibrium of the system is unique.
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.
