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
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 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
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
The global exponentially stability and the existence of periodic solutions of a class of Hopfield neural networks with time delays are investigated. By constructing a novel Lyapunov function, new criteria are provided...The global exponentially stability and the existence of periodic solutions of a class of Hopfield neural networks with time delays are investigated. By constructing a novel Lyapunov function, new criteria are provided to guarantee the global exponentially stability of such systems. For the delayed Hopfield neural networks with time-varying external inputs, new criteria are also acquired for the existence and exponentially stability of periodic solutions. The results are generalizations and improvements of some recent achievements reported in the literature on networks with time delays.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
Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constru...Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.展开更多
In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium poin...In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of Hopfield neural network models with distributed time delays are studied. Using M-matrix theory and constructing proper Liapunov functionals, the sufficient conditions for global asymptotic stability are obtained.展开更多
A class of Hopfield neural network with time-varying delays and impulsive effects is concerned. By applying the piecewise continuous vector Lyapunov function some sufficient conditions were obtained to ensure the glob...A class of Hopfield neural network with time-varying delays and impulsive effects is concerned. By applying the piecewise continuous vector Lyapunov function some sufficient conditions were obtained to ensure the global exponential stability of impulsive delay neural networks. An example and its simulation are given to illustrate the effectiveness of the results.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
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
In this paper, Hopfield neural networks with impulse and leakage time-varying delay are considered. New sufficient conditions for global asymptotical stability of the equilibrium point are derived by using Lyapunov-Kr...In this paper, Hopfield neural networks with impulse and leakage time-varying delay are considered. New sufficient conditions for global asymptotical stability of the equilibrium point are derived by using Lyapunov-Kravsovskii functional, model transformation and some analysis techniques. The criterion of stability depends on the impulse and the bounds of the leakage time-varying delay and its derivative, and is presented in terms of a linear matrix inequality (LMI).展开更多
In this paper, we investigate the robust exponential stability of a class of fractional order Hopfield neural network with Caputo derivative, and we get some sufficient conditions to guarantee its robust exponential s...In this paper, we investigate the robust exponential stability of a class of fractional order Hopfield neural network with Caputo derivative, and we get some sufficient conditions to guarantee its robust exponential stability. Finally, we use one numerical simulation example to illustrate the correctness and effectiveness 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
In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as...In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.展开更多
The global asymptotic stability for Hopfield neural networks with time delay was investigated, A theorem and two corollaries were obtained, in which the boundedness and differentiability of f(j) on R in some articles ...The global asymptotic stability for Hopfield neural networks with time delay was investigated, A theorem and two corollaries were obtained, in which the boundedness and differentiability of f(j) on R in some articles were deleted. Some sufficient conditions for the existence of global asymptotic stable equilibrium of the networks in this paper are better than the sufficient conditions in quoted articles.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
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.
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.
基金the Science Foundation of Guangdong Province in China
文摘The global exponentially stability and the existence of periodic solutions of a class of Hopfield neural networks with time delays are investigated. By constructing a novel Lyapunov function, new criteria are provided to guarantee the global exponentially stability of such systems. For the delayed Hopfield neural networks with time-varying external inputs, new criteria are also acquired for the existence and exponentially stability of periodic solutions. The results are generalizations and improvements of some recent achievements reported in the literature on networks with time delays.
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Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.
基金Supported by the National Natural Science Foundation of China(No.59935100)
文摘In this paper, without assuming the boundedness, monotonicity and differentiability of the activation functions, the conditions ensuring existence, uniqueness, and global asymptotical stability of the equilibrium point of Hopfield neural network models with distributed time delays are studied. Using M-matrix theory and constructing proper Liapunov functionals, the sufficient conditions for global asymptotic stability are obtained.
基金Project supported by the National Natural Science Foundation of China (No. 10371083)
文摘A class of Hopfield neural network with time-varying delays and impulsive effects is concerned. By applying the piecewise continuous vector Lyapunov function some sufficient conditions were obtained to ensure the global exponential stability of impulsive delay neural networks. An example and its simulation are given to illustrate the effectiveness of the results.
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 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.
文摘In this paper, Hopfield neural networks with impulse and leakage time-varying delay are considered. New sufficient conditions for global asymptotical stability of the equilibrium point are derived by using Lyapunov-Kravsovskii functional, model transformation and some analysis techniques. The criterion of stability depends on the impulse and the bounds of the leakage time-varying delay and its derivative, and is presented in terms of a linear matrix inequality (LMI).
基金Supported by the Natural Science Foundation of Shandong Province(Grant No.ZR2011FQ002)
文摘In this paper, we investigate the robust exponential stability of a class of fractional order Hopfield neural network with Caputo derivative, and we get some sufficient conditions to guarantee its robust exponential stability. Finally, we use one numerical simulation example to illustrate the correctness and effectiveness of our results.
基金Supported by the National Natural Science Foundation of P.R.China(60274017,60572070,60325311)the Natural Science Foundation of Liaoning Province(20022030)
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.
基金Supported by the Innovation Platform Open Fund in Hunan Province Colleges and Universities of China(201485).
文摘In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.
文摘The global asymptotic stability for Hopfield neural networks with time delay was investigated, A theorem and two corollaries were obtained, in which the boundedness and differentiability of f(j) on R in some articles were deleted. Some sufficient conditions for the existence of global asymptotic stable equilibrium of the networks in this paper are better than the sufficient conditions in quoted articles.
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.
