Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two o...Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two open problems and extend some known results.展开更多
A class of n-dimensional ODEs with up to n feedbacks from the n’th variable is analysed. The feedbacks are represented by non-specific, bounded, non-negative C<sup>1</sup> functions. The main result is th...A class of n-dimensional ODEs with up to n feedbacks from the n’th variable is analysed. The feedbacks are represented by non-specific, bounded, non-negative C<sup>1</sup> functions. The main result is the formulation and proof of an easily applicable criterion for existence of a globally stable fixed point of the system. The proof relies on the contraction mapping theorem. Applications of this type of systems are numerous in biology, e.g., models of the hypothalamic-pituitary-adrenal axis and testosterone secretion. Some results important for modelling are: 1) Existence of an attractive trapping region. This is a bounded set with non-negative elements where solutions cannot escape. All solutions are shown to converge to a “minimal” trapping region. 2) At least one fixed point exists. 3) Sufficient criteria for a unique fixed point are formulated. One case where this is fulfilled is when the feedbacks are negative.展开更多
Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constru...Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.展开更多
In this paper we prove a global attractivity result for the unique positive equilibrium point of a difference equation,which improves and generalizes some known ones in the existing literature.Especially,our results c...In this paper we prove a global attractivity result for the unique positive equilibrium point of a difference equation,which improves and generalizes some known ones in the existing literature.Especially,our results completely solve an open problem and some conjectures proposed in[1,2,3,4].展开更多
The global stability, boundedness and dissipation are studied with respect to partial variables of the following nonlinear autonomous systems: and applications of these results are described to the absolute stability ...The global stability, boundedness and dissipation are studied with respect to partial variables of the following nonlinear autonomous systems: and applications of these results are described to the absolute stability of the Lurie-type control system, the Yacubovich-type control system and the global stability of the Volterra ecological systems.展开更多
We are concerned with a class of neutral stochastic partial differential equations driven by Rosenblatt process in a Hilbert space. By combining some stochastic analysis techniques, tools from semigroup theory, and st...We are concerned with a class of neutral stochastic partial differential equations driven by Rosenblatt process in a Hilbert space. By combining some stochastic analysis techniques, tools from semigroup theory, and stochastic integral inequalities, we identify the global attracting sets of this kind of equations. Especially, some sufficient conditions ensuring the exponent p-stability of mild solutions to the stochastic systems under investigation are obtained. Last, an example is given to illustrate the theory in the work.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 the global attractivity of the nonlinear difference equationis investigated, where a,b, A ∈ (0,∞), k is an positive integer and the initial conditions x- k, …, x-1 and x0 are arbitrary positive number...In this paper the global attractivity of the nonlinear difference equationis investigated, where a,b, A ∈ (0,∞), k is an positive integer and the initial conditions x- k, …, x-1 and x0 are arbitrary positive numbers. It is shown that the unique positive equilibrium of the equation is global attractive. As a corollary, the result gives a positive confirmation on the conjecture presented by Kocic and Ladas [1,p154].展开更多
In this paper, a stochastic two-prey one-predator model with <em>S</em>-type distributed time delays and Lévy noises is considered. Using the comparison theorem and Ito’s formula, sufficient conditio...In this paper, a stochastic two-prey one-predator model with <em>S</em>-type distributed time delays and Lévy noises is considered. Using the comparison theorem and Ito’s formula, sufficient conditions of persistence in the mean and extinct for each population are established. Then, conditions of global attractivity and stability in distribution by Barbalat’s conclusion are also obtained. Furthermore, Euler numerical simulation method is given to demonstrate our conclusions.展开更多
The study suggests asymptotic behavior of the solution to a new class of difference equations: . where a, bi, α and β are positive real numbers for i = 0, 1, · · · , k , and the initial conditions ψ-...The study suggests asymptotic behavior of the solution to a new class of difference equations: . where a, bi, α and β are positive real numbers for i = 0, 1, · · · , k , and the initial conditions ψ-j, ψ-j+1, · · ·, ψ0 are randomly positive real numbers where j = 2k + 1. Accordingly, we consider the stability, boundedness and periodicity of the solutions of this recursive sequence. Indeed, we give some interesting counter examples in order to verify our strong results.展开更多
This paper is devoted to dealing with the parabolic-elliptic-elliptic attraction-repulsion chemotaxis system.We aim to understand the competition among the repulsion,the attraction,the nonlinear productions and give c...This paper is devoted to dealing with the parabolic-elliptic-elliptic attraction-repulsion chemotaxis system.We aim to understand the competition among the repulsion,the attraction,the nonlinear productions and give conditions of global existence and blow-up for the two-dimensional attraction-repulsion chemotaxis system。展开更多
In this paper, we investigate some qualitative behavior of the solutions of the difference equation where the coefficients a, b and c<sub>i</sub> are positive real numbers, and where the initial conditions...In this paper, we investigate some qualitative behavior of the solutions of the difference equation where the coefficients a, b and c<sub>i</sub> are positive real numbers, and where the initial conditions are arbitrary positive real numbers.展开更多
文摘Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two open problems and extend some known results.
文摘A class of n-dimensional ODEs with up to n feedbacks from the n’th variable is analysed. The feedbacks are represented by non-specific, bounded, non-negative C<sup>1</sup> functions. The main result is the formulation and proof of an easily applicable criterion for existence of a globally stable fixed point of the system. The proof relies on the contraction mapping theorem. Applications of this type of systems are numerous in biology, e.g., models of the hypothalamic-pituitary-adrenal axis and testosterone secretion. Some results important for modelling are: 1) Existence of an attractive trapping region. This is a bounded set with non-negative elements where solutions cannot escape. All solutions are shown to converge to a “minimal” trapping region. 2) At least one fixed point exists. 3) Sufficient criteria for a unique fixed point are formulated. One case where this is fulfilled is when the feedbacks are negative.
文摘Some global properties such as global attractivity and global exponential stability for delayed Hopfield neural networks model, under the weaker assumptions on nonlinear activation functions, are concerned. By constructing suitable Liapunov function, some simpler criteria for global attractivity and global exponential stability for Hopfield continuous neural network,; with time delays are presented.
基金the National Natural Science Foundation of China(61473340)the Distinguished Professor Foundation of Qianjiang Scholar in Zhejiang Province+1 种基金the National Natural Science Foundation of Zhejiang Province(LQ13A010019)the National Natural Science Foundation of Zhejiang University of Science and Technology(F701108G14).
文摘In this paper we prove a global attractivity result for the unique positive equilibrium point of a difference equation,which improves and generalizes some known ones in the existing literature.Especially,our results completely solve an open problem and some conjectures proposed in[1,2,3,4].
基金Project supported by the National Natural Science Foundation of China
文摘The global stability, boundedness and dissipation are studied with respect to partial variables of the following nonlinear autonomous systems: and applications of these results are described to the absolute stability of the Lurie-type control system, the Yacubovich-type control system and the global stability of the Volterra ecological systems.
文摘We are concerned with a class of neutral stochastic partial differential equations driven by Rosenblatt process in a Hilbert space. By combining some stochastic analysis techniques, tools from semigroup theory, and stochastic integral inequalities, we identify the global attracting sets of this kind of equations. Especially, some sufficient conditions ensuring the exponent p-stability of mild solutions to the stochastic systems under investigation are obtained. Last, an example is given to illustrate the theory in the work.
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 the global attractivity of the nonlinear difference equationis investigated, where a,b, A ∈ (0,∞), k is an positive integer and the initial conditions x- k, …, x-1 and x0 are arbitrary positive numbers. It is shown that the unique positive equilibrium of the equation is global attractive. As a corollary, the result gives a positive confirmation on the conjecture presented by Kocic and Ladas [1,p154].
文摘In this paper, a stochastic two-prey one-predator model with <em>S</em>-type distributed time delays and Lévy noises is considered. Using the comparison theorem and Ito’s formula, sufficient conditions of persistence in the mean and extinct for each population are established. Then, conditions of global attractivity and stability in distribution by Barbalat’s conclusion are also obtained. Furthermore, Euler numerical simulation method is given to demonstrate our conclusions.
文摘The study suggests asymptotic behavior of the solution to a new class of difference equations: . where a, bi, α and β are positive real numbers for i = 0, 1, · · · , k , and the initial conditions ψ-j, ψ-j+1, · · ·, ψ0 are randomly positive real numbers where j = 2k + 1. Accordingly, we consider the stability, boundedness and periodicity of the solutions of this recursive sequence. Indeed, we give some interesting counter examples in order to verify our strong results.
基金The NSF(11301419)of Chinathe Meritocracy Research Funds(17YC382)of China West Normal University
文摘This paper is devoted to dealing with the parabolic-elliptic-elliptic attraction-repulsion chemotaxis system.We aim to understand the competition among the repulsion,the attraction,the nonlinear productions and give conditions of global existence and blow-up for the two-dimensional attraction-repulsion chemotaxis system。
文摘In this paper, we investigate some qualitative behavior of the solutions of the difference equation where the coefficients a, b and c<sub>i</sub> are positive real numbers, and where the initial conditions are arbitrary positive real numbers.
