Deep learning has been recognized as an effective method for indoor positioning.However,most existing real-valued neural networks(RVNNs)treat the two constituent components of complex-valued channel state information(...Deep learning has been recognized as an effective method for indoor positioning.However,most existing real-valued neural networks(RVNNs)treat the two constituent components of complex-valued channel state information(CSI)as real-valued inputs,potentially discarding useful information embedded in the original CSI.In addition,existing positioning models generally face the contradiction between computational complexity and positioning accuracy.To address these issues,we combine graph neural network(GNN)with complex-valued neural network(CVNN)to construct a lightweight indoor positioning model named CGNet.CGNet employs complexvalued convolution operation to directly process the original CSI data,fully exploiting the correlation between real and imaginary parts of CSI while extracting local features.Subsequently,the feature values are treated as nodes,and conditional position encoding(CPE)module is applied to add positional information.To reduce the number of connections in the graph structure and lower themodel complexity,feature information is mapped to an efficient graph structure through a dynamic axial graph construction(DAGC)method,with global features extracted usingmaximum relative graph convolution(MRConv).Experimental results show that,on the CTW dataset,CGNet achieves a 10%improvement in positioning accuracy compared to existing methods,while the number of model parameters is only 0.8 M.CGNet achieves excellent positioning accuracy with very few parameters.展开更多
Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts ...Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.展开更多
In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. S...In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks. One numerical example is provided to show the effectiveness and superiority of the presented results.展开更多
Recently,deep learning has been used to establish the nonlinear and nonintuitive mapping between physical structures and electromagnetic responses of meta-atoms for higher computational efficiency.However,to obtain su...Recently,deep learning has been used to establish the nonlinear and nonintuitive mapping between physical structures and electromagnetic responses of meta-atoms for higher computational efficiency.However,to obtain sufficiently accurate predictions,the conventional deep-learning-based method consumes excessive time to collect the data set,thus hindering its wide application in this interdisciplinary field.We introduce a spectral transfer-learning-based metasurface design method to achieve excellent performance on a small data set with only 1000 samples in the target waveband by utilizing open-source data from another spectral range.We demonstrate three transfer strategies and experimentally quantify their performance,among which the“frozen-none”robustly improves the prediction accuracy by∼26%compared to direct learning.We propose to use a complex-valued deep neural network during the training process to further improve the spectral predicting precision by∼30%compared to its real-valued counterparts.We design several typical teraherz metadevices by employing a hybrid inverse model consolidating this trained target network and a global optimization algorithm.The simulated results successfully validate the capability of our approach.Our work provides a universal methodology for efficient and accurate metasurface design in arbitrary wavebands,which will pave the way toward the automated and mass production of metasurfaces.展开更多
This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks(FOCVCNNs)with time-delay.The chaotic behaviors of a class of fractional-order complex-valued neural ...This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks(FOCVCNNs)with time-delay.The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated.Meanwhile,based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems,a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks.Finally,the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.展开更多
In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition,...In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.展开更多
Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks(FCVMNNs) with time delay is investigated. Firstly, based on the complex-valu...Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks(FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag-Leffler synchronization(FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time(SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly,some simulation examples are designed to verify the validity of conclusions.展开更多
In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued n...In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points, and the complex-valued neural network cannot be easily influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results.展开更多
Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network mode...Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is ad- vanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs’ stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).展开更多
To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which inte...To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.展开更多
In order to improve the bidirectional associative memory(BAM) performance, a modified BAM model(MBAM) is used to enhance neural network(NN)’s memory capacity and error correction capability, theoretical analysis and ...In order to improve the bidirectional associative memory(BAM) performance, a modified BAM model(MBAM) is used to enhance neural network(NN)’s memory capacity and error correction capability, theoretical analysis and experiment results illuminate that MBAM performs much better than the original BAM. The MBAM is used in computer numeric control(CNC) machine fault diagnosis, it not only can complete fault diagnosis correctly but also have fairly high error correction capability for disturbed Input Information sequence.Moreover MBAM model is a more convenient and effective method of solving the problem of CNC electric system fault diagnosis.展开更多
Without assuming the smoothness,monotonicity and boundedness of the activation functions, some novel criteria on the existence and global exponential stability of equilibrium point for delayed bidirectional associativ...Without assuming the smoothness,monotonicity and boundedness of the activation functions, some novel criteria on the existence and global exponential stability of equilibrium point for delayed bidirectional associative memory (BAM) neural networks are established by applying the Liapunov functional methods and matrix_algebraic techniques. It is shown that the new conditions presented in terms of a nonsingular M matrix described by the networks parameters,the connection matrix and the Lipschitz constant of the activation functions,are not only simple and practical,but also easier to check and less conservative than those imposed by similar results in recent literature.展开更多
Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix...Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality（LMI） conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.展开更多
Sufficient conditions to guarantee the existence and global exponential stability of periodic solutions of a Cohen-Grossberg-type BAM neural network are established by suitable mathematical transformation.
In this paper, based on the theory of fractional-order calculus, we obtain some sufficient conditions for the uniform stability of fractional-order fuzzy BAM neural networks with delays in the leakage terms. Moreover,...In this paper, based on the theory of fractional-order calculus, we obtain some sufficient conditions for the uniform stability of fractional-order fuzzy BAM neural networks with delays in the leakage terms. Moreover, the existence, uniqueness and stability of its equilibrium point are also proved. A numerical example is presented to demonstrate the validity and feasibility of the proposed results.展开更多
Based on the theory of fractional calculus, the contraction mapping principle, Krasnoselskii fixed point theorem and the inequality technique, a class of Caputo fractional-order BAM neural networks with delays in the ...Based on the theory of fractional calculus, the contraction mapping principle, Krasnoselskii fixed point theorem and the inequality technique, a class of Caputo fractional-order BAM neural networks with delays in the leakage terms is investigated in this paper. Some new sufficient conditions are established to guarantee the existence and uniqueness of the nontrivial solution. Moreover, uniform stability of such networks is proposed in fixed time intervals. Finally, an illustrative example is also given to demonstrate the effectiveness of the obtained results.展开更多
In this paper,a class of fuzzy BAM neural networks with time varying delays is discussed.By using the properties of M-matrix,Linear Matrix Inequality(LMI)approach and general Lyapunov-Krasovskii functional,some new su...In this paper,a class of fuzzy BAM neural networks with time varying delays is discussed.By using the properties of M-matrix,Linear Matrix Inequality(LMI)approach and general Lyapunov-Krasovskii functional,some new sufficient conditions are derived to ensure the existence of periodic solutions and the global exponential stability of the fuzzy BAM neural networks with time varying delays.These results have important significance in the design of global exponential stable BAM networks with delays.Moreover,an example is given to illustrate that the conditions of the results in the paper are feasible.展开更多
By employing the Lyapunov stability theory and linear matrix inequality（LMI）technique,delay-dependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory（BAM）neu...By employing the Lyapunov stability theory and linear matrix inequality（LMI）technique,delay-dependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory（BAM）neural networks with time-varying delays.The proposed condition can be checked easily by LMI control toolbox in Matlab.A numerical example is given to demonstrate the effectiveness of our results.展开更多
For a tridiagonal two-layer real six-neuron model,the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature.In the present paper,we extend this two-layer...For a tridiagonal two-layer real six-neuron model,the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature.In the present paper,we extend this two-layer real six-neuron network model into a complex-valued delayed network model.Based on the mathematical analysis method,some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established under the assumption that the activation function can be separated into its real and imaginary parts.Our sufficient conditions obtained by the mathematical analysis method in this paper are simpler than those obtained by the Hopf bifurcation method.Computer simulation is provided to illustrate the correctness of the theoretical results.展开更多
文摘Deep learning has been recognized as an effective method for indoor positioning.However,most existing real-valued neural networks(RVNNs)treat the two constituent components of complex-valued channel state information(CSI)as real-valued inputs,potentially discarding useful information embedded in the original CSI.In addition,existing positioning models generally face the contradiction between computational complexity and positioning accuracy.To address these issues,we combine graph neural network(GNN)with complex-valued neural network(CVNN)to construct a lightweight indoor positioning model named CGNet.CGNet employs complexvalued convolution operation to directly process the original CSI data,fully exploiting the correlation between real and imaginary parts of CSI while extracting local features.Subsequently,the feature values are treated as nodes,and conditional position encoding(CPE)module is applied to add positional information.To reduce the number of connections in the graph structure and lower themodel complexity,feature information is mapped to an efficient graph structure through a dynamic axial graph construction(DAGC)method,with global features extracted usingmaximum relative graph convolution(MRConv).Experimental results show that,on the CTW dataset,CGNet achieves a 10%improvement in positioning accuracy compared to existing methods,while the number of model parameters is only 0.8 M.CGNet achieves excellent positioning accuracy with very few parameters.
基金partially supported by the JSPS KAKENHI(JP22H03643,JP19K22891)。
文摘Complex-valued neural networks(CVNNs)have shown their excellent efficiency compared to their real counterparts in speech enhancement,image and signal processing.Researchers throughout the years have made many efforts to improve the learning algorithms and activation functions of CVNNs.Since CVNNs have proven to have better performance in handling the naturally complex-valued data and signals,this area of study will grow and expect the arrival of some effective improvements in the future.Therefore,there exists an obvious reason to provide a comprehensive survey paper that systematically collects and categorizes the advancement of CVNNs.In this paper,we discuss and summarize the recent advances based on their learning algorithms,activation functions,which is the most challenging part of building a CVNN,and applications.Besides,we outline the structure and applications of complex-valued convolutional,residual and recurrent neural networks.Finally,we also present some challenges and future research directions to facilitate the exploration of the ability of CVNNs.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61503338,61573316,61374152,and 11302195)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ15F030005)
文摘In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks. One numerical example is provided to show the effectiveness and superiority of the presented results.
基金support from the National Natural Science Foundation of China (Grant Nos.62027820,61975143,61735012,and 62205380).
文摘Recently,deep learning has been used to establish the nonlinear and nonintuitive mapping between physical structures and electromagnetic responses of meta-atoms for higher computational efficiency.However,to obtain sufficiently accurate predictions,the conventional deep-learning-based method consumes excessive time to collect the data set,thus hindering its wide application in this interdisciplinary field.We introduce a spectral transfer-learning-based metasurface design method to achieve excellent performance on a small data set with only 1000 samples in the target waveband by utilizing open-source data from another spectral range.We demonstrate three transfer strategies and experimentally quantify their performance,among which the“frozen-none”robustly improves the prediction accuracy by∼26%compared to direct learning.We propose to use a complex-valued deep neural network during the training process to further improve the spectral predicting precision by∼30%compared to its real-valued counterparts.We design several typical teraherz metadevices by employing a hybrid inverse model consolidating this trained target network and a global optimization algorithm.The simulated results successfully validate the capability of our approach.Our work provides a universal methodology for efficient and accurate metasurface design in arbitrary wavebands,which will pave the way toward the automated and mass production of metasurfaces.
基金Project supported by the Science and Technology Support Program of Xingtai,China(Grant No.2019ZC054)。
文摘This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks(FOCVCNNs)with time-delay.The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated.Meanwhile,based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems,a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks.Finally,the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61374094 and 61503338)the Natural Science Foundation of Zhejiang Province,China(Grant No.LQ15F030005)
文摘In this paper, the multistability issue is discussed for delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions. Based on a fixed theorem and stability definition, sufficient criteria are established for the existence and stability of multiple equilibria of complex-valued recurrent neural networks. The number of stable equilibria is larger than that of real-valued recurrent neural networks, which can be used to achieve high-capacity associative memories. One numerical example is provided to show the effectiveness and superiority of the presented results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 62176189 and 62106181)the Hubei Province Key Laboratory of Systems Science in Metallurgical Process (Wuhan University of Science and Technology) (Grant No. Y202002)。
文摘Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks(FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag-Leffler synchronization(FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time(SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly,some simulation examples are designed to verify the validity of conclusions.
文摘In this paper, the singularity and its effect on learning dynamics in the complex-valued neural network are elucidated. It has learned that the linear combination structure in the updating rule of the complex-valued neural network increases the speed of moving away from the singular points, and the complex-valued neural network cannot be easily influenced by the singular points, whereas the learning of the usual real-valued neural network can be attracted in the neighborhood of singular points, which causes a standstill in learning. Simulation results on the learning dynamics of the three-layered real-valued and complex-valued neural networks in the neighborhood of singularities support the analytical results.
基金Project (No. 60074008) supported by the National Natural Science Foundation of China
文摘Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is ad- vanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs’ stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).
基金Project (No. 60074008) supported by the National Natural Science Foundation of China
文摘To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.
文摘In order to improve the bidirectional associative memory(BAM) performance, a modified BAM model(MBAM) is used to enhance neural network(NN)’s memory capacity and error correction capability, theoretical analysis and experiment results illuminate that MBAM performs much better than the original BAM. The MBAM is used in computer numeric control(CNC) machine fault diagnosis, it not only can complete fault diagnosis correctly but also have fairly high error correction capability for disturbed Input Information sequence.Moreover MBAM model is a more convenient and effective method of solving the problem of CNC electric system fault diagnosis.
文摘Without assuming the smoothness,monotonicity and boundedness of the activation functions, some novel criteria on the existence and global exponential stability of equilibrium point for delayed bidirectional associative memory (BAM) neural networks are established by applying the Liapunov functional methods and matrix_algebraic techniques. It is shown that the new conditions presented in terms of a nonsingular M matrix described by the networks parameters,the connection matrix and the Lipschitz constant of the activation functions,are not only simple and practical,but also easier to check and less conservative than those imposed by similar results in recent literature.
基金Supported by the National Natural Science Foundation of China (6067402760875039)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education (20050446001)Scientific Research Foundation of Qufu Normal University
文摘Several novel stability conditions for BAM neural networks with time-varying delays are studied.Based on Lyapunov-Krasovskii functional combined with linear matrix inequality approach,the delay-dependent linear matrix inequality（LMI） conditions are established to guarantee robust asymptotic stability for given delayed BAM neural networks.These criteria can be easily verified by utilizing the recently developed algorithms for solving LMIs.A numerical example is provided to demonstrate the effectiveness and less conservatism of the main results.
文摘Sufficient conditions to guarantee the existence and global exponential stability of periodic solutions of a Cohen-Grossberg-type BAM neural network are established by suitable mathematical transformation.
文摘In this paper, based on the theory of fractional-order calculus, we obtain some sufficient conditions for the uniform stability of fractional-order fuzzy BAM neural networks with delays in the leakage terms. Moreover, the existence, uniqueness and stability of its equilibrium point are also proved. A numerical example is presented to demonstrate the validity and feasibility of the proposed results.
文摘Based on the theory of fractional calculus, the contraction mapping principle, Krasnoselskii fixed point theorem and the inequality technique, a class of Caputo fractional-order BAM neural networks with delays in the leakage terms is investigated in this paper. Some new sufficient conditions are established to guarantee the existence and uniqueness of the nontrivial solution. Moreover, uniform stability of such networks is proposed in fixed time intervals. Finally, an illustrative example is also given to demonstrate the effectiveness of the obtained results.
基金Supported by the National Natural Science Foundation of China(60574043)the Science Foundation of the Education Committee of Hunan Province(06C792+1 种基金07C700)the Construction Program of Key Disciplines in Hunan Province,Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan province
文摘In this paper,a class of fuzzy BAM neural networks with time varying delays is discussed.By using the properties of M-matrix,Linear Matrix Inequality(LMI)approach and general Lyapunov-Krasovskii functional,some new sufficient conditions are derived to ensure the existence of periodic solutions and the global exponential stability of the fuzzy BAM neural networks with time varying delays.These results have important significance in the design of global exponential stable BAM networks with delays.Moreover,an example is given to illustrate that the conditions of the results in the paper are feasible.
基金supported by Natural Science Foundation of Hebei Province under Grant No.E2007000381
文摘By employing the Lyapunov stability theory and linear matrix inequality（LMI）technique,delay-dependent stability criterion is derived to ensure the exponential stability of bi-directional associative memory（BAM）neural networks with time-varying delays.The proposed condition can be checked easily by LMI control toolbox in Matlab.A numerical example is given to demonstrate the effectiveness of our results.
文摘For a tridiagonal two-layer real six-neuron model,the Hopf bifurcation was investigated by studying the eigenvalue equations of the related linear system in the literature.In the present paper,we extend this two-layer real six-neuron network model into a complex-valued delayed network model.Based on the mathematical analysis method,some sufficient conditions to guarantee the existence of periodic oscillatory solutions are established under the assumption that the activation function can be separated into its real and imaginary parts.Our sufficient conditions obtained by the mathematical analysis method in this paper are simpler than those obtained by the Hopf bifurcation method.Computer simulation is provided to illustrate the correctness of the theoretical results.
