In this paper the transmission of leptospirosis, an infectious disease caused by bacteria, is studied. Leptospirosis is currently spreading in Thailand and worldwide. A Susceptible-Infected-Removed sir model is used t...In this paper the transmission of leptospirosis, an infectious disease caused by bacteria, is studied. Leptospirosis is currently spreading in Thailand and worldwide. A Susceptible-Infected-Removed sir model is used to study the stability analysis, analytical solution and global behavior of the spreading of the disease. The model was analysed using the techniques of non-linear dynamical systems. Two equilibrium points were found and the stability conditions for these equilibrium points were established. It will be shown that the linearised solutions of the sir equations are in good agreement with numerical solutions.展开更多
This paper considers the drive-response synchronization in finite-time and fixed-time of inertial neural networks with time-varying and distributed delays(mixed delays). First, by constructing a proper variable substi...This paper considers the drive-response synchronization in finite-time and fixed-time of inertial neural networks with time-varying and distributed delays(mixed delays). First, by constructing a proper variable substitution, the original inertial neural networks can be rewritten as a first-order differential system. Second, by constructing Lyapunov functions and using differential inequalities,some new and effective criteria are obtained for ensuring the finite-time synchronization. Finally, three numerical examples are also given at the end of this paper to show the effectiveness of the results.展开更多
This article is concerned with the finite-time stabilization(FTSB) of a class of delayed-Hopfield neural networks with a timevarying delay in the leakage term in the presence of parameter uncertainties. To accomplish ...This article is concerned with the finite-time stabilization(FTSB) of a class of delayed-Hopfield neural networks with a timevarying delay in the leakage term in the presence of parameter uncertainties. To accomplish the target of FTSB, two new finitetime controllers are designed for uncertain delayed-Hopfield neural networks with a time-varying delay in the leakage term. By utilizing the finite-time stability theory and the Lyapunov-Krasovskii functional(LKF) approach, some sufficient conditions for the FTSB of these neural networks are established. These conditions, which can be used for the selection of control parameters,are in the form of linear matrix inequalities(LMIs) and can be numerically checked. Additionally, an upper bound of the settling time was estimated. Finally, our theoretical results are further substantiated by two numerical examples with graphical illustrations to demonstrate the effectiveness of the results.展开更多
The models of competitive neural network(CNN)was in recent past proposed to describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications,where there are two types of memories:Long-term mem...The models of competitive neural network(CNN)was in recent past proposed to describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications,where there are two types of memories:Long-term memories(LTM)and short-term memories(STM),LTM presents unsupervised and slow synaptic modifications and STM characterize the fast neural activity.This paper is concerned with a class of neutral type CNN’s with mixed delay and D operator.By employing the appropriate differential inequality theory,some sufficient conditions are given to ensure that all solutions of the model converge exponentially to zero vector.Finally,an illustrative example is also given at the end of this paper to show the effectiveness of the proposed results.展开更多
This paper is concerned with an interval general Cohen-Grossberg bidirectional associative memory neural networks with mixed delays. Under proper conditions, the authors studied the existence,the uniqueness and the gl...This paper is concerned with an interval general Cohen-Grossberg bidirectional associative memory neural networks with mixed delays. Under proper conditions, the authors studied the existence,the uniqueness and the global exponential stability of almost automorphic solutions for the suggested system. The proposed method was mainly based on the exponential dichotomy of linear differential equation, the Banach’s fixed point principle and the differential inequality techniques. The authors illustrate with an example to demonstrate the effectiveness of the proposed findings.展开更多
In this paper,a neutral Hopfield neural network with bidirectional connection is considered.In the first step,by choosing the connection weights as parameters bifurcation,the critical point at which a zero root of mul...In this paper,a neutral Hopfield neural network with bidirectional connection is considered.In the first step,by choosing the connection weights as parameters bifurcation,the critical point at which a zero root of multiplicity two occurs in the characteristic equation associated with the linearized system.In the second step,we studied the zeros of a third degree exponential polynomial in order to make sure that except the double zero root,all the other roots of the characteristic equation have real parts that are negative.Moreover,we find the critical values to guarantee the existence of the Bogdanov–Takens bifurcation.In the third step,the normal form is obtained and its dynamical behaviors are studied after the use of the reduction on the center manifold and the theory of the normal form.Furthermore,for the demonstration of our results,we have given a numerical example.展开更多
In this paper, we consider the existence, the uniqueness, the global exponential stability, the global asymptotic stability, the uniform asymptotic stability and the uniform stability of the equilibrium point of impul...In this paper, we consider the existence, the uniqueness, the global exponential stability, the global asymptotic stability, the uniform asymptotic stability and the uniform stability of the equilibrium point of impulsive competitive neural networks with distributed delays and leakage time-varying delays. The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem. By finding suitable Lyapunov-Krasovskii functional, some sufficient conditions are derived ensuring some kinds of stability. Finally, several examples and their simulations are given to illustrate the effectiveness of the obtained results.展开更多
In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalities on manifolds with non-convex boundary.
In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compac...In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compact, we get a classification result. We also discuss the relation with quasi-Einstein manifolds.展开更多
In this manuscript, we studied a class of delayed Fuzzy Genetic Regulatory Networks (FGRNs) with Stepanov-like weighted pseudo almost automorphic coefficients. New criteria for the existence, uniqueness and global exp...In this manuscript, we studied a class of delayed Fuzzy Genetic Regulatory Networks (FGRNs) with Stepanov-like weighted pseudo almost automorphic coefficients. New criteria for the existence, uniqueness and global exponential stability of its weighted pseudo almost automorphic solution are established. Our approach is based on Banach fixed point theorem and novel analysis techniques. Moreover, a numerical example is given to illustrate the validity of the obtained results.展开更多
We investigate convergence properties of random Taylor series whose coefficients are ψ-mixing random variables. In particular, we give sufficient conditions such that the circle of convergence of the series forms alm...We investigate convergence properties of random Taylor series whose coefficients are ψ-mixing random variables. In particular, we give sufficient conditions such that the circle of convergence of the series forms almost surely a natural boundary.展开更多
文摘In this paper the transmission of leptospirosis, an infectious disease caused by bacteria, is studied. Leptospirosis is currently spreading in Thailand and worldwide. A Susceptible-Infected-Removed sir model is used to study the stability analysis, analytical solution and global behavior of the spreading of the disease. The model was analysed using the techniques of non-linear dynamical systems. Two equilibrium points were found and the stability conditions for these equilibrium points were established. It will be shown that the linearised solutions of the sir equations are in good agreement with numerical solutions.
文摘This paper considers the drive-response synchronization in finite-time and fixed-time of inertial neural networks with time-varying and distributed delays(mixed delays). First, by constructing a proper variable substitution, the original inertial neural networks can be rewritten as a first-order differential system. Second, by constructing Lyapunov functions and using differential inequalities,some new and effective criteria are obtained for ensuring the finite-time synchronization. Finally, three numerical examples are also given at the end of this paper to show the effectiveness of the results.
文摘This article is concerned with the finite-time stabilization(FTSB) of a class of delayed-Hopfield neural networks with a timevarying delay in the leakage term in the presence of parameter uncertainties. To accomplish the target of FTSB, two new finitetime controllers are designed for uncertain delayed-Hopfield neural networks with a time-varying delay in the leakage term. By utilizing the finite-time stability theory and the Lyapunov-Krasovskii functional(LKF) approach, some sufficient conditions for the FTSB of these neural networks are established. These conditions, which can be used for the selection of control parameters,are in the form of linear matrix inequalities(LMIs) and can be numerically checked. Additionally, an upper bound of the settling time was estimated. Finally, our theoretical results are further substantiated by two numerical examples with graphical illustrations to demonstrate the effectiveness of the results.
文摘The models of competitive neural network(CNN)was in recent past proposed to describe the dynamics of cortical cognitive maps with unsupervised synaptic modifications,where there are two types of memories:Long-term memories(LTM)and short-term memories(STM),LTM presents unsupervised and slow synaptic modifications and STM characterize the fast neural activity.This paper is concerned with a class of neutral type CNN’s with mixed delay and D operator.By employing the appropriate differential inequality theory,some sufficient conditions are given to ensure that all solutions of the model converge exponentially to zero vector.Finally,an illustrative example is also given at the end of this paper to show the effectiveness of the proposed results.
文摘This paper is concerned with an interval general Cohen-Grossberg bidirectional associative memory neural networks with mixed delays. Under proper conditions, the authors studied the existence,the uniqueness and the global exponential stability of almost automorphic solutions for the suggested system. The proposed method was mainly based on the exponential dichotomy of linear differential equation, the Banach’s fixed point principle and the differential inequality techniques. The authors illustrate with an example to demonstrate the effectiveness of the proposed findings.
文摘In this paper,a neutral Hopfield neural network with bidirectional connection is considered.In the first step,by choosing the connection weights as parameters bifurcation,the critical point at which a zero root of multiplicity two occurs in the characteristic equation associated with the linearized system.In the second step,we studied the zeros of a third degree exponential polynomial in order to make sure that except the double zero root,all the other roots of the characteristic equation have real parts that are negative.Moreover,we find the critical values to guarantee the existence of the Bogdanov–Takens bifurcation.In the third step,the normal form is obtained and its dynamical behaviors are studied after the use of the reduction on the center manifold and the theory of the normal form.Furthermore,for the demonstration of our results,we have given a numerical example.
文摘In this paper, we consider the existence, the uniqueness, the global exponential stability, the global asymptotic stability, the uniform asymptotic stability and the uniform stability of the equilibrium point of impulsive competitive neural networks with distributed delays and leakage time-varying delays. The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem. By finding suitable Lyapunov-Krasovskii functional, some sufficient conditions are derived ensuring some kinds of stability. Finally, several examples and their simulations are given to illustrate the effectiveness of the obtained results.
基金supported by Fonds National de la Recherche Luxembourg(Grant No.O14/7628746 GEOMREV)the University of Luxembourg(Grant No.IRP R-AGR-0517-10/AGSDE)+1 种基金supported by National Natural Science Foundation of China(Grant No.11501508)Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ16A010009)
文摘In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalities on manifolds with non-convex boundary.
基金supported by NSFC(Grant No.11171143)Zhejiang Provincial Natural Science Foundation of China(Project No.LY13A010009 and LY14A010021)supported by the Fonds National de la Recherche Luxembourg(OPEN Project GEOMREV)
文摘In this paper, we study gradient solitons to the Ricci flow coupled with harmonic map heat flow. We derive new identities on solitons similar to those on gradient solitons of the Ricci flow. When the soliton is compact, we get a classification result. We also discuss the relation with quasi-Einstein manifolds.
文摘In this manuscript, we studied a class of delayed Fuzzy Genetic Regulatory Networks (FGRNs) with Stepanov-like weighted pseudo almost automorphic coefficients. New criteria for the existence, uniqueness and global exponential stability of its weighted pseudo almost automorphic solution are established. Our approach is based on Banach fixed point theorem and novel analysis techniques. Moreover, a numerical example is given to illustrate the validity of the obtained results.
基金supported by National Natural Science Foundation of China (Grant No. 11501127).supported by National Natural Science Foundation of China (Grant No. 11801591)supported by the Luxembourg National Research Fund (FNR) (Grant No. R-AGR-3410-12-Z)Science and Technology Program of Guangzhou (Grant No. 202002030369)
文摘We investigate convergence properties of random Taylor series whose coefficients are ψ-mixing random variables. In particular, we give sufficient conditions such that the circle of convergence of the series forms almost surely a natural boundary.
