Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjectur...Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture forward.展开更多
The global attractivity of the delay difference equation Deltax(n) + a(n)x(n) + f(n, Sigma(s = -k)(0)(q) over bar (s), (n) x(s + n)) = 0, which includes the discrete type of many mathematical ecological equations, was...The global attractivity of the delay difference equation Deltax(n) + a(n)x(n) + f(n, Sigma(s = -k)(0)(q) over bar (s), (n) x(s + n)) = 0, which includes the discrete type of many mathematical ecological equations, was discussed. The sufficient conditions that guarantee every solution to converge to zero are obtained. Many known results are improved and generated.展开更多
In this paper we further study the delay differential equation N（t） = - δN（t） + pN（t -τ）e<sup>（-aN）（g-τ）</sup>,t≥0 （*）used in describing the dynamics of Nicholson’s blowflies. When p】δ, ...In this paper we further study the delay differential equation N（t） = - δN（t） + pN（t -τ）e<sup>（-aN）（g-τ）</sup>,t≥0 （*）used in describing the dynamics of Nicholson’s blowflies. When p】δ, We establish newsufficient conditions for the positive equilibrium N<sup>*</sup> of （*） which is a global attractor. Ourcriteria improve correspondent results obtained by Kulenovic, Ladas and Sficas [1], and Soand Yu [2].展开更多
The asymptotic behavior of a class of nonlinear delay difference equation wax studied . Some sufficient conditions are obtained for permanence and global attractivity . The results can be applied to a claxs of nonline...The asymptotic behavior of a class of nonlinear delay difference equation wax studied . Some sufficient conditions are obtained for permanence and global attractivity . The results can be applied to a claxs of nonlinear delay difference equations and to the delay discrete Logistic model and some known results are included.展开更多
A new sufficient condition is given for the global attractivity of solutions ofthe delay difference equation xn+1= xnf(xn, zn-1), n = 0,1…,As an application, ourresults partly confirm a conjecture of G. Ladas.
This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n=0,1,2,...,(*)where {p n} is a sequence of positive real n...This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n=0,1,2,...,(*)where {p n} is a sequence of positive real numbers, {τ(n)} is a nondecreasing sequence of integers, τ(n)<n and lim n→∞τ(n)=∞ .It is proved that ifnj=τ(n)p j≤54 for sufficiently large n and ∞j=0p j=∞,then all positive solutions of Eq.(*) tend to 1 as n→∞ .The results improve the existing results in literature.展开更多
This paper is intended to investigate a class of Nicholson's blowflies system with patch structure and multiple pairs of distinct time-varying delays,we are interested in finding the infuence of the distinct time-...This paper is intended to investigate a class of Nicholson's blowflies system with patch structure and multiple pairs of distinct time-varying delays,we are interested in finding the infuence of the distinct time-varying delays in the same reproductive function on its asymptotic behavior.By using the theory of functional differential equations,the fluctuation lemma,and the technique of differential inequalities,some new delay-dependent criteria on the global attractivity of the positive equilibrium point are established.In addition,the effectiveness and feasibility of the theoretical achievements are illustrated by some numerical simulations.展开更多
Consider the delay difference equationNn+1-Nn = - δNn + pNn-kexp(-aNn-k), n = 0,1,2,... (*)where δ ∈ (0,1), p,a ∈ (0,∞) and k ∈ N. We obtain a sufficient condition for all positive solutions of (*) to be attract...Consider the delay difference equationNn+1-Nn = - δNn + pNn-kexp(-aNn-k), n = 0,1,2,... (*)where δ ∈ (0,1), p,a ∈ (0,∞) and k ∈ N. We obtain a sufficient condition for all positive solutions of (*) to be attracted to its positive equilibrium N* for p > δ. It improves a correspondent result obtained by Kocic and Ladas [1].展开更多
In this paper we further study the delay differential equation N .(t)=-δN(t)+pN(t-τ)e -aN(t-τ) , t0(*) used in describing the dynamics of Nicholson’s blowflies. When p】δ ,we establish new su...In this paper we further study the delay differential equation N .(t)=-δN(t)+pN(t-τ)e -aN(t-τ) , t0(*) used in describing the dynamics of Nicholson’s blowflies. When p】δ ,we establish new sufficient conditions for the positive equilibrium N * of (*) which is a global attractor.展开更多
Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to...Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to be attracted to its equilibrium N is obtained.It improves correspondent result obtained by Chen and Yu in 1999.展开更多
Here several theorems are established to discuss uniform stability and uniformasymptotical stability of zero solution for difference equations with time delay. Thesetheorems extend Razumikhin Method from functional di...Here several theorems are established to discuss uniform stability and uniformasymptotical stability of zero solution for difference equations with time delay. Thesetheorems extend Razumikhin Method from functional differential equations to time delaydifference equations.展开更多
文摘Several new sufficient conditions are given for the global attractivity of solutions of a kind of delay difference equations. They either include or improve some known results and put the study of Ladas' conjecture forward.
文摘The global attractivity of the delay difference equation Deltax(n) + a(n)x(n) + f(n, Sigma(s = -k)(0)(q) over bar (s), (n) x(s + n)) = 0, which includes the discrete type of many mathematical ecological equations, was discussed. The sufficient conditions that guarantee every solution to converge to zero are obtained. Many known results are improved and generated.
基金Science Foundation of Hunan Educational Committee.
文摘In this paper we further study the delay differential equation N（t） = - δN（t） + pN（t -τ）e<sup>（-aN）（g-τ）</sup>,t≥0 （*）used in describing the dynamics of Nicholson’s blowflies. When p】δ, We establish newsufficient conditions for the positive equilibrium N<sup>*</sup> of （*） which is a global attractor. Ourcriteria improve correspondent results obtained by Kulenovic, Ladas and Sficas [1], and Soand Yu [2].
基金Foundation items: the National Natural Science Foundation of China (10171040)the Natural Science Foundation of Gansu Province of China (ZS011-A25-007-Z)+1 种基金 the Foundation for University Key Teacher by Ministry of Education of China the Teaching and Re
文摘The asymptotic behavior of a class of nonlinear delay difference equation wax studied . Some sufficient conditions are obtained for permanence and global attractivity . The results can be applied to a claxs of nonlinear delay difference equations and to the delay discrete Logistic model and some known results are included.
基金Supported by the NNSFC(10071022),Mathematical Tianyuan Foundation of China(Ty10026002-01-05-03)Shanghai Priority Academic Discipline.
文摘A new sufficient condition is given for the global attractivity of solutions ofthe delay difference equation xn+1= xnf(xn, zn-1), n = 0,1…,As an application, ourresults partly confirm a conjecture of G. Ladas.
文摘This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n=0,1,2,...,(*)where {p n} is a sequence of positive real numbers, {τ(n)} is a nondecreasing sequence of integers, τ(n)<n and lim n→∞τ(n)=∞ .It is proved that ifnj=τ(n)p j≤54 for sufficiently large n and ∞j=0p j=∞,then all positive solutions of Eq.(*) tend to 1 as n→∞ .The results improve the existing results in literature.
基金This work was supposed by Jiaxing public welfare research program(2022AD30113).
文摘This paper is intended to investigate a class of Nicholson's blowflies system with patch structure and multiple pairs of distinct time-varying delays,we are interested in finding the infuence of the distinct time-varying delays in the same reproductive function on its asymptotic behavior.By using the theory of functional differential equations,the fluctuation lemma,and the technique of differential inequalities,some new delay-dependent criteria on the global attractivity of the positive equilibrium point are established.In addition,the effectiveness and feasibility of the theoretical achievements are illustrated by some numerical simulations.
文摘Consider the delay difference equationNn+1-Nn = - δNn + pNn-kexp(-aNn-k), n = 0,1,2,... (*)where δ ∈ (0,1), p,a ∈ (0,∞) and k ∈ N. We obtain a sufficient condition for all positive solutions of (*) to be attracted to its positive equilibrium N* for p > δ. It improves a correspondent result obtained by Kocic and Ladas [1].
文摘In this paper we further study the delay differential equation N .(t)=-δN(t)+pN(t-τ)e -aN(t-τ) , t0(*) used in describing the dynamics of Nicholson’s blowflies. When p】δ ,we establish new sufficient conditions for the positive equilibrium N * of (*) which is a global attractor.
基金Supported by the Science Foundation of Educational Committee of Hunan Province
文摘Consider the discrete Lasota Wazewska modelN n+1 -N n =-μN n +pe -rN n-k , n=0,1,2,...(*)where μ∈(0,1),r,p∈(0,∞) and k ∈N.A sufficient condition for all positive solutions of (*) to be attracted to its equilibrium N is obtained.It improves correspondent result obtained by Chen and Yu in 1999.
文摘Here several theorems are established to discuss uniform stability and uniformasymptotical stability of zero solution for difference equations with time delay. Thesetheorems extend Razumikhin Method from functional differential equations to time delaydifference equations.
