This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment ...This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.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
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,we study the anti-periodic solutions for a class of impulsive Cohen-Grossberg neural networks with mixed delays.By using analysis techniques,some sufficient conditions are obtained which guarantee the ex...In this paper,we study the anti-periodic solutions for a class of impulsive Cohen-Grossberg neural networks with mixed delays.By using analysis techniques,some sufficient conditions are obtained which guarantee the existence and global exponential stability of the anti-periodic solutions.The criteria extend and improve some earlier results.Moreover,we give an examples to illustrate our main results.展开更多
This paper studies the global exponential p-norm stability of bidirectional associative memory(BAM)neural networks with unbounded time-varying delays.A novel method based on the representation of solutions is put forw...This paper studies the global exponential p-norm stability of bidirectional associative memory(BAM)neural networks with unbounded time-varying delays.A novel method based on the representation of solutions is put forward to deduce a global exponential p-norm stability criterion.This method does not need to set up any Lyapunov-Krasovskii functionals(LKF),which can greatly reduce a large amount of computations and is simpler than the existing methods.In the end,representative numerical examples are given to llustrate the availability of the method.展开更多
In this paper, we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprisi...In this paper, we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprising different discrete and distributed time delays. Some sufficient conditions are given for the existence and the global exponential stability of the weighted pseudo almost-periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper complement the previously known ones. Finally, an illustrative example is given to demonstrate the effectiveness of our results.展开更多
In this paper we consider the initial Neumann boundary value problem for a degenerate Keller-Segel model which features a signal-dependent non-increasing motility function.The main obstacle of analysis comes from the ...In this paper we consider the initial Neumann boundary value problem for a degenerate Keller-Segel model which features a signal-dependent non-increasing motility function.The main obstacle of analysis comes from the possible degeneracy when the signal concentration becomes unbounded.In the current work,we are interested in the boundedness and exponential stability of the classical solution in higher dimensions.With the aid of a Lyapunov functional and a delicate Alikakos-Moser type iteration,we are able to establish a time-independent upper bound of the concentration provided that the motility function decreases algebraically.Then we further prove the uniform-in-time boundedness of the solution by constructing an estimation involving a weighted energy.Finally,thanks to the Lyapunov functional again,we prove the exponential stabilization toward the spatially homogeneous steady states.Our boundedness result improves those in[1]and the exponential stabilization is obtained for the first time.展开更多
By using the Leray-Schauder fixed point theorem,differential inequality techniques and constructing suitable Lyapunov functional,several sufficient conditions are obtained for the existence and global exponential stab...By using the Leray-Schauder fixed point theorem,differential inequality techniques and constructing suitable Lyapunov functional,several sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general shunting inhibitory cellular neural networks with delays.Some new results are obtained and some previously known results are improved.An example is employed to illustrate our feasible results.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
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
In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction ...In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.展开更多
A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and...A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.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
The importance of prediction for genetic regulatory network(GRNs)makes mathematical modeling a prominent tool.In this paper,we consider weighted pseudo-almost periodic solutions for a class of GRNs with time-varying d...The importance of prediction for genetic regulatory network(GRNs)makes mathematical modeling a prominent tool.In this paper,we consider weighted pseudo-almost periodic solutions for a class of GRNs with time-varying delays.We establish the existence,uniqueness,and global exponential stability by employing the theory of dichotomy,the fixed point theorem,and differential inequality.A numerical example along with a graphical illustration are presented to support our main results.Our results extend existing GRNs models using almost periodic functions to support a wider range of regulatory processes.展开更多
Using the energy estimate and Gagliardo-Nirenberg-type inequalities,the existence and uniform boundedness of the global solutions to a strongly coupled reaction-diffusion system are proved. This system is a generaliza...Using the energy estimate and Gagliardo-Nirenberg-type inequalities,the existence and uniform boundedness of the global solutions to a strongly coupled reaction-diffusion system are proved. This system is a generalization of the two-species Lotka-Volterra predator-prey model with self and cross-diffusion. Suffcient condition for the global asymptotic stability of the positive equilibrium point of the model is given by constructing Lyapunov function.展开更多
In this paper, by using phase space (Ch,|·|h) (in short, space Ch) defined in [1], we study the existence on the bounded solutions and the almost periodic solutions for functional differential equations with in...In this paper, by using phase space (Ch,|·|h) (in short, space Ch) defined in [1], we study the existence on the bounded solutions and the almost periodic solutions for functional differential equations with infinite delay. By combining properties of space Ch and some techniques of Liapunov functional, we show that the h-exponentially asymptotical stability of solutions for the equations implies the existence of the bounded solutions and it guarantees the existence of the almost periodic solutions for the equations.展开更多
In this paper, we study the existence, uniqueness, and the global exponential stability of the periodic solution and equilibrium of hybrid bidirectional associative memory neural networks with discrete delays. By inge...In this paper, we study the existence, uniqueness, and the global exponential stability of the periodic solution and equilibrium of hybrid bidirectional associative memory neural networks with discrete delays. By ingeniously importing real parameters di > 0 (i = 1,2, …, n) which can be adjusted, making use of the Lyapunov functional method and some analysis techniques, some new sufficient conditions are established. Our results generalize and improve the related results in [9]. These conditions can be used both to design globally exponentially stable and periodical oscillatory hybrid bidirectional associative neural networks with discrete delays, and to enlarge the area of designing neural networks. Our work has important significance in related theory and its application.展开更多
文摘This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.
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.
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supported by National Nature Science Foundation under Grant 11161029,Chinascience and technology research projects of guangxi under Grant 2013YB282,201203YB186
文摘In this paper,we study the anti-periodic solutions for a class of impulsive Cohen-Grossberg neural networks with mixed delays.By using analysis techniques,some sufficient conditions are obtained which guarantee the existence and global exponential stability of the anti-periodic solutions.The criteria extend and improve some earlier results.Moreover,we give an examples to illustrate our main results.
基金supported in part by the Natural Science Foundation of Heilongjiang Province (No.YQ2021F014)the Fundamental Research Funds for the provincial universities of Heilongjiang Province (No.2020-KYYWF-1040)。
文摘This paper studies the global exponential p-norm stability of bidirectional associative memory(BAM)neural networks with unbounded time-varying delays.A novel method based on the representation of solutions is put forward to deduce a global exponential p-norm stability criterion.This method does not need to set up any Lyapunov-Krasovskii functionals(LKF),which can greatly reduce a large amount of computations and is simpler than the existing methods.In the end,representative numerical examples are given to llustrate the availability of the method.
文摘In this paper, we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprising different discrete and distributed time delays. Some sufficient conditions are given for the existence and the global exponential stability of the weighted pseudo almost-periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper complement the previously known ones. Finally, an illustrative example is given to demonstrate the effectiveness of our results.
基金supported by Hubei Provincial Natural Science Foundation(2020CFB602).
文摘In this paper we consider the initial Neumann boundary value problem for a degenerate Keller-Segel model which features a signal-dependent non-increasing motility function.The main obstacle of analysis comes from the possible degeneracy when the signal concentration becomes unbounded.In the current work,we are interested in the boundedness and exponential stability of the classical solution in higher dimensions.With the aid of a Lyapunov functional and a delicate Alikakos-Moser type iteration,we are able to establish a time-independent upper bound of the concentration provided that the motility function decreases algebraically.Then we further prove the uniform-in-time boundedness of the solution by constructing an estimation involving a weighted energy.Finally,thanks to the Lyapunov functional again,we prove the exponential stabilization toward the spatially homogeneous steady states.Our boundedness result improves those in[1]and the exponential stabilization is obtained for the first time.
基金Supported by the Honghe University Master or Doctor Initial Fund (Grant No.XSS07001)the Scientific Research Fund of Yunnan Provincial Education Department (Grant No.07Y10085)
文摘By using the Leray-Schauder fixed point theorem,differential inequality techniques and constructing suitable Lyapunov functional,several sufficient conditions are obtained for the existence and global exponential stability of periodic solutions for general shunting inhibitory cellular neural networks with delays.Some new results are obtained and some previously known results are improved.An example is employed to illustrate our feasible results.
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In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.
文摘A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.
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.
文摘The importance of prediction for genetic regulatory network(GRNs)makes mathematical modeling a prominent tool.In this paper,we consider weighted pseudo-almost periodic solutions for a class of GRNs with time-varying delays.We establish the existence,uniqueness,and global exponential stability by employing the theory of dichotomy,the fixed point theorem,and differential inequality.A numerical example along with a graphical illustration are presented to support our main results.Our results extend existing GRNs models using almost periodic functions to support a wider range of regulatory processes.
基金Partially supported by the National Natural Science Foundation of China (10671158)the NSFof Gansu Province (3ZS061-A25-015)+1 种基金the Scientific Research Fund of Gansu Provincial Educatio nDepartment (0601-21)NWNU-KJCXGC-03-18, 39 Foundations
文摘Using the energy estimate and Gagliardo-Nirenberg-type inequalities,the existence and uniform boundedness of the global solutions to a strongly coupled reaction-diffusion system are proved. This system is a generalization of the two-species Lotka-Volterra predator-prey model with self and cross-diffusion. Suffcient condition for the global asymptotic stability of the positive equilibrium point of the model is given by constructing Lyapunov function.
文摘In this paper, by using phase space (Ch,|·|h) (in short, space Ch) defined in [1], we study the existence on the bounded solutions and the almost periodic solutions for functional differential equations with infinite delay. By combining properties of space Ch and some techniques of Liapunov functional, we show that the h-exponentially asymptotical stability of solutions for the equations implies the existence of the bounded solutions and it guarantees the existence of the almost periodic solutions for the equations.
基金This work was supported by scientific research foundation of affairs concerning national living abroad office of the State Council.
文摘In this paper, we study the existence, uniqueness, and the global exponential stability of the periodic solution and equilibrium of hybrid bidirectional associative memory neural networks with discrete delays. By ingeniously importing real parameters di > 0 (i = 1,2, …, n) which can be adjusted, making use of the Lyapunov functional method and some analysis techniques, some new sufficient conditions are established. Our results generalize and improve the related results in [9]. These conditions can be used both to design globally exponentially stable and periodical oscillatory hybrid bidirectional associative neural networks with discrete delays, and to enlarge the area of designing neural networks. Our work has important significance in related theory and its application.