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, we employ a fixed point theorem due to Krasnosel’skii to attain the existence of periodic solutions for neutral-type neural networks with delays on a periodic time scale. Some new sufficient conditions...In this paper, we employ a fixed point theorem due to Krasnosel’skii to attain the existence of periodic solutions for neutral-type neural networks with delays on a periodic time scale. Some new sufficient conditions are established to show that there exists a unique periodic solution by the contraction mapping principle.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
Traditional biological neural networks cannot simulate the real situation of the abrupt synaptic connections between neurons while modeling associative memory of human brains.In this paper,the memristive multidirectio...Traditional biological neural networks cannot simulate the real situation of the abrupt synaptic connections between neurons while modeling associative memory of human brains.In this paper,the memristive multidirectional associative memory neural networks(MAMNNs)with mixed time-varying delays are investigated in the sense of Filippov solution.First,three steps are given to prove the existence of the almost periodic solution.Two new lemmas are proposed to prove the boundness of the solution and the asymptotical almost periodicity of the solution by constructing Lyapunov function.Second,the uniqueness and global exponential stability of the almost periodic solution of memristive MAMNNs are investigated by a new Lyapunov function.The sufficient conditions guaranteeing the properties of almost periodic solution are derived based on the relevant definitions,Halanay inequality and Lyapunov function.The investigation is an extension of the research on the periodic solution and almost periodic solution of bidirectional associative memory neural networks.Finally,numerical examples with simulations are presented to show the validity of the main results.展开更多
In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generaliz...In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.展开更多
In this paper, a class of fuzzy cellular neural networks with distributed delays is discussed. By employing fixed point theorem and inequality techniques, some sufficient conditions are obtained to ensure the existenc...In this paper, a class of fuzzy cellular neural networks with distributed delays is discussed. By employing fixed point theorem and inequality techniques, some sufficient conditions are obtained to ensure the existence and global exponential stability of periodic solutions to the systems. Without assuming the global Lipschitz conditions of activation functions, our results are novel and reduce the limitation of previous known results. Moreover, an example is given to illustrate the effectiveness of our results.展开更多
By using the continuation theorem of Mawhin's coincidence degree theory, Hoelder inequality and some analysis techniques, some effective results are obtained ensuring existence and global exponential stability of per...By using the continuation theorem of Mawhin's coincidence degree theory, Hoelder inequality and some analysis techniques, some effective results are obtained ensuring existence and global exponential stability of periodic solutions in delayed cellular neural networks with impulses. An illustrative example is given to demonstrate the effectiveness of the obtained results.展开更多
In this paper,a class of bidirectional associative memory(BAM) recurrent neural networks with delays are studied.By a fixed point theorem and a Lyapunov functional,some new sufficient conditions for the existence,uniq...In this paper,a class of bidirectional associative memory(BAM) recurrent neural networks with delays are studied.By a fixed point theorem and a Lyapunov functional,some new sufficient conditions for the existence,uniqueness and global exponential stability of the almost periodic solutions are established.These conditions are easy to be verified and our results complement the previous known results.展开更多
In this paper,Hopfield neural networks with delays and impulses are considered.By means of mathematical analysis techniques,some sufficient conditions for the existence of positive almost periodic solutions are obtained.
A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov function-als, introducing many...A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov function-als, introducing many parameters qij* , rij* , qij, rij∈ R and wi】0 (i, j = 1, 2, …, n) and combining them with the elementary inequality 2ab≤a2 + b2 technique. These criteria have important significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, the results in literature are extended and improved. Two examples are given to illustrate the theory.展开更多
The principle aim of this paper is to explore the existence of periodic solution of neural networks model with neutral delay. Sufficient and realistic conditions are obtained by means of an abstract continuous theorem...The principle aim of this paper is to explore the existence of periodic solution of neural networks model with neutral delay. Sufficient and realistic conditions are obtained by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.展开更多
This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed poin...This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed point theorem and differential inequality techniques,the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks.The results are completely new.Finally,the authors give an example to illustrate the feasibility of the results.展开更多
In this paper, a class of two-dimensional shunting inhibitory cellular neural networks with distributed delays and variable coefficients system dxij/dt=-αij(t)xij-∑↑ckl∈Nr(i,j)cij^kl(t)fkl(∫0^+∞pkl(s)...In this paper, a class of two-dimensional shunting inhibitory cellular neural networks with distributed delays and variable coefficients system dxij/dt=-αij(t)xij-∑↑ckl∈Nr(i,j)cij^kl(t)fkl(∫0^+∞pkl(s)xkl(t-s)ds)xij+Lij(t) is studied. By using the Schauder's fixed point theorem and Lyapunov function, we obtain some sufficient conditions about the existence and attractivity of almost periodic solutions to the above system, and all its solutions converge to such almost periodic solution. An example is given to illustrate that the conditions of our results are feasible.展开更多
This paper,mainly explores a class of non-autonomous inertial neural networks with proportional delays and time-varying coefficients.By combining Lyapunov function method with differential inequality approach,non-redu...This paper,mainly explores a class of non-autonomous inertial neural networks with proportional delays and time-varying coefficients.By combining Lyapunov function method with differential inequality approach,non-reduced order method is used to establish some novel assertions on the existence and generalized exponential stability of periodic solutions for the addressed model.In addition,an example and its numerical simulations are given to support the proposed approach.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
In this paper, we study Cohen-Grossberg neural networks (CGNN) with time-varying delay. Based on Halanay inequality and continuation theorem of the coincidence degree, we obtain some sufficient conditions ensuring t...In this paper, we study Cohen-Grossberg neural networks (CGNN) with time-varying delay. Based on Halanay inequality and continuation theorem of the coincidence degree, we obtain some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of periodic solution. Our results complement previously known results.展开更多
By using the continuation theorem of Mawhin's coincidence degree theory and the Liapunov func tional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stab...By using the continuation theorem of Mawhin's coincidence degree theory and the Liapunov func tional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the periodic solution to the BAM-type Cohen-Grossberg neural networks involving timevarying delays.展开更多
Purpose–The purpose of this paper is to investigate the weighted pseudo-almost periodic solutions of shunting inhibitory cellular neural networks(SICNNs)with time-varying delays and distributed delays.Design/methodol...Purpose–The purpose of this paper is to investigate the weighted pseudo-almost periodic solutions of shunting inhibitory cellular neural networks(SICNNs)with time-varying delays and distributed delays.Design/methodology/approach–The principle of weighted pseudo-almost periodic functions and some new mathematical analysis skills are applied.Findings–A set of sufficient criteria which guarantee the existence and exponential stability of the weighted pseudo-almost periodic solutions of the considered SICNNs are established.Originality/value–The derived results of this paper are new and complement some earlier works.The innovation of this paper concludes two points:a new sufficient criteria guaranteeing the existence and exponential stability of the weighted pseudo-almost periodic solutions of SICNNs are established;and the ideas of this paper can be applied to investigate some other similar neural networks.展开更多
Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neur...Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.展开更多
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, we employ a fixed point theorem due to Krasnosel’skii to attain the existence of periodic solutions for neutral-type neural networks with delays on a periodic time scale. Some new sufficient conditions are established to show that there exists a unique periodic solution by the contraction mapping principle.
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supported by the Beijing Municipal Natural Science Foundation(No.4202025)partially sponsored by the National Natural Science Foundation of China(No.61672070)the Beijing Municipal Education Commission(No.KZ201910005008).
文摘Traditional biological neural networks cannot simulate the real situation of the abrupt synaptic connections between neurons while modeling associative memory of human brains.In this paper,the memristive multidirectional associative memory neural networks(MAMNNs)with mixed time-varying delays are investigated in the sense of Filippov solution.First,three steps are given to prove the existence of the almost periodic solution.Two new lemmas are proposed to prove the boundness of the solution and the asymptotical almost periodicity of the solution by constructing Lyapunov function.Second,the uniqueness and global exponential stability of the almost periodic solution of memristive MAMNNs are investigated by a new Lyapunov function.The sufficient conditions guaranteeing the properties of almost periodic solution are derived based on the relevant definitions,Halanay inequality and Lyapunov function.The investigation is an extension of the research on the periodic solution and almost periodic solution of bidirectional associative memory neural networks.Finally,numerical examples with simulations are presented to show the validity of the main results.
文摘In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.
基金the National Natural Science Foundation of China underGrant No.60574043the National Science Foundation of Hunan Provincial Education Departmentunder Grant No.06C792 and No.07C700the construct program of the key discipline in HunanProvince.
文摘In this paper, a class of fuzzy cellular neural networks with distributed delays is discussed. By employing fixed point theorem and inequality techniques, some sufficient conditions are obtained to ensure the existence and global exponential stability of periodic solutions to the systems. Without assuming the global Lipschitz conditions of activation functions, our results are novel and reduce the limitation of previous known results. Moreover, an example is given to illustrate the effectiveness of our results.
基金Foundation item: the National Natural Science Foundation of China (No. 10671158) NWNU-KJCXGC-212 and GS-55-CXRC.
文摘By using the continuation theorem of Mawhin's coincidence degree theory, Hoelder inequality and some analysis techniques, some effective results are obtained ensuring existence and global exponential stability of periodic solutions in delayed cellular neural networks with impulses. An illustrative example is given to demonstrate the effectiveness of the obtained results.
文摘In this paper,a class of bidirectional associative memory(BAM) recurrent neural networks with delays are studied.By a fixed point theorem and a Lyapunov functional,some new sufficient conditions for the existence,uniqueness and global exponential stability of the almost periodic solutions are established.These conditions are easy to be verified and our results complement the previous known results.
文摘In this paper,Hopfield neural networks with delays and impulses are considered.By means of mathematical analysis techniques,some sufficient conditions for the existence of positive almost periodic solutions are obtained.
文摘A set of criteria are presented for the global exponential stability and the existence of periodic solutions of delayed cellular neural networks (DCNNs) by constructing suitable Lyapunov function-als, introducing many parameters qij* , rij* , qij, rij∈ R and wi】0 (i, j = 1, 2, …, n) and combining them with the elementary inequality 2ab≤a2 + b2 technique. These criteria have important significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. In addition, the results in literature are extended and improved. Two examples are given to illustrate the theory.
文摘The principle aim of this paper is to explore the existence of periodic solution of neural networks model with neutral delay. Sufficient and realistic conditions are obtained by means of an abstract continuous theorem of k-set contractive operator and some analysis technique.
基金supported by the National Natural Sciences Foundation of People’s Republic of China under Grants Nos.11861072 and 11361072.
文摘This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed point theorem and differential inequality techniques,the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks.The results are completely new.Finally,the authors give an example to illustrate the feasibility of the results.
基金This work was supported by the Foundation of Hunan Provincial Education Department(04C613, 03C009, 05A057).
文摘In this paper, a class of two-dimensional shunting inhibitory cellular neural networks with distributed delays and variable coefficients system dxij/dt=-αij(t)xij-∑↑ckl∈Nr(i,j)cij^kl(t)fkl(∫0^+∞pkl(s)xkl(t-s)ds)xij+Lij(t) is studied. By using the Schauder's fixed point theorem and Lyapunov function, we obtain some sufficient conditions about the existence and attractivity of almost periodic solutions to the above system, and all its solutions converge to such almost periodic solution. An example is given to illustrate that the conditions of our results are feasible.
基金the National Natural Science Foundation of China(Nos.71471020 and 51839002)Hunan Provincial Natural Science Foundation of China(No.2016.J.J1001)Scientific Research Fund of Hunan Provincial Education Department(No.15A003).
文摘This paper,mainly explores a class of non-autonomous inertial neural networks with proportional delays and time-varying coefficients.By combining Lyapunov function method with differential inequality approach,non-reduced order method is used to establish some novel assertions on the existence and generalized exponential stability of periodic solutions for the addressed model.In addition,an example and its numerical simulations are given to support the proposed approach.
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.
基金Supported by the National Natural Science Foundation of China (No. 11071060)Key Program of Application Science Foundation of Hunan Province (No. 2008FJ2008)
文摘In this paper, we study Cohen-Grossberg neural networks (CGNN) with time-varying delay. Based on Halanay inequality and continuation theorem of the coincidence degree, we obtain some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of periodic solution. Our results complement previously known results.
基金Supported by the National Natural Science Foundation of China (No. 10971173)the Scientific Research Foundation of Hunan Provincial Educational Department (No. 05A057)+1 种基金supported by the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Provincethe Construct Program of the Key Discipline in Hunan Province
文摘By using the continuation theorem of Mawhin's coincidence degree theory and the Liapunov func tional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the periodic solution to the BAM-type Cohen-Grossberg neural networks involving timevarying delays.
文摘Purpose–The purpose of this paper is to investigate the weighted pseudo-almost periodic solutions of shunting inhibitory cellular neural networks(SICNNs)with time-varying delays and distributed delays.Design/methodology/approach–The principle of weighted pseudo-almost periodic functions and some new mathematical analysis skills are applied.Findings–A set of sufficient criteria which guarantee the existence and exponential stability of the weighted pseudo-almost periodic solutions of the considered SICNNs are established.Originality/value–The derived results of this paper are new and complement some earlier works.The innovation of this paper concludes two points:a new sufficient criteria guaranteeing the existence and exponential stability of the weighted pseudo-almost periodic solutions of SICNNs are established;and the ideas of this paper can be applied to investigate some other similar neural networks.
文摘Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.