In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are establishe...In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delay.展开更多
Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function,...Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function, the Lyapunov functional or the Beuman-Bihari inequality, and some sufficient conditions based on those properties are given. Finally, the conclusions are applied to over-voltage models based on three-phase nonsynchronous closing of switches appearing in the power systems, the results in accord with the background physical meaning are obtained. And all the conditions of the conclusions are easy to validate, so the conclusions have definite theoretical meaning and are easy to apply in practice.展开更多
Consider the second order nonlinear neutral delay differential equaiton[α(t)|(x(t)+p(t)x(t-τ))′| α-1 (x(t)+p(t)x(t-τ))′]′+q(t)|x(t-σ)| α-1 x(t-σ)=0. We obtain a sufficient condition for the oscillati...Consider the second order nonlinear neutral delay differential equaiton[α(t)|(x(t)+p(t)x(t-τ))′| α-1 (x(t)+p(t)x(t-τ))′]′+q(t)|x(t-σ)| α-1 x(t-σ)=0. We obtain a sufficient condition for the oscillation of all solutions of the above equation, our result extend and improve the result in .展开更多
Some new sufficient conditions for the oscillation of the neutral equationddt[y（t）-R（t）y（t-r）]+P（t）y（t-τ）- Q（t）y（t-σ）=0, where P,Q,R∈C（[t0,∞）,R+) and r,τ,σ∈（0,∞）,are obtained for the case whe...Some new sufficient conditions for the oscillation of the neutral equationddt[y（t）-R（t）y（t-r）]+P（t）y（t-τ）- Q（t）y（t-σ）=0, where P,Q,R∈C（[t0,∞）,R+) and r,τ,σ∈（0,∞）,are obtained for the case where former results can not be applied in this paper.展开更多
In this paper, the sufficient conditions for the oscillation of all solutions of certain second order nonlinea neutral equations with continuous distributed delay.
This paper is concerned with oscillatory behavior of a class of fourth-order delay dynamic equations on a time scale.In the general time scales case,four oscillation theorems are presented that can be used in cases wh...This paper is concerned with oscillatory behavior of a class of fourth-order delay dynamic equations on a time scale.In the general time scales case,four oscillation theorems are presented that can be used in cases where known results fail to apply.The results obtained can be applied to an equation which is referred to as Swift-Hohenberg delay equation on a time scale.These criteria improve a number of related contributions to the subject.Some illustrative examples are provided.展开更多
In this paper, following a previous paper （[32] Permanence and extinction of a non- autonomous HIV-I model with two time delays, preprint） on the permanence and extinc- tion of a delayed non-autonomous HIV-1 within-...In this paper, following a previous paper （[32] Permanence and extinction of a non- autonomous HIV-I model with two time delays, preprint） on the permanence and extinc- tion of a delayed non-autonomous HIV-1 within-host model, we introduce and investigate a delayed HIV-1 model including maximum homeostatic proliferation rate of CD4＋ T- cells and varying coefficients. By applying the asymptotic analysis theory and oscillation theory, we show： （i） the system will be permanent when the threshold value R. 〉 1, and for this case we also obtain the explicit estimate of the eventual lower bound of the HIV-1 virus load; （ii） the threshold value R＊ 〈 1 implies the extinction of the virus. Furthermore, we obtain that the threshold dynamics is in agreement with that of the corresponding autonomous system, which extends the classic results for the system with constant coefficients. Numerical simulations are also given to illustrate our main results, and in particular, some sensitivity test of R. is established.展开更多
In this paper, we consider a Cohen-Grossberg neural network with three delays. Regard- ing time delays as a parameter, we investigate the effect of time delays on its dynamics. We show that there exist stability switc...In this paper, we consider a Cohen-Grossberg neural network with three delays. Regard- ing time delays as a parameter, we investigate the effect of time delays on its dynamics. We show that there exist stability switches for time delays under certain conditions and the conditions for the existence of periodic oscillations are given by discussing the associated characteristic equation. Numerical simulations are given to illustrate the obtained results and interesting network behaviors are observed, such as multiple stability switches of the network equilibrium and synchronous （asynchronous） oscillations.展开更多
文摘In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delay.
文摘Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function, the Lyapunov functional or the Beuman-Bihari inequality, and some sufficient conditions based on those properties are given. Finally, the conclusions are applied to over-voltage models based on three-phase nonsynchronous closing of switches appearing in the power systems, the results in accord with the background physical meaning are obtained. And all the conditions of the conclusions are easy to validate, so the conclusions have definite theoretical meaning and are easy to apply in practice.
文摘Consider the second order nonlinear neutral delay differential equaiton[α(t)|(x(t)+p(t)x(t-τ))′| α-1 (x(t)+p(t)x(t-τ))′]′+q(t)|x(t-σ)| α-1 x(t-σ)=0. We obtain a sufficient condition for the oscillation of all solutions of the above equation, our result extend and improve the result in .
文摘Some new sufficient conditions for the oscillation of the neutral equationddt[y（t）-R（t）y（t-r）]+P（t）y（t-τ）- Q（t）y（t-σ）=0, where P,Q,R∈C（[t0,∞）,R+) and r,τ,σ∈（0,∞）,are obtained for the case where former results can not be applied in this paper.
文摘In this paper, the sufficient conditions for the oscillation of all solutions of certain second order nonlinea neutral equations with continuous distributed delay.
基金supported by National Key Basic Research Program of China (Grant No. 2013CB035604)National Natural Science Foundation of China (Grant Nos. 61034007, 51277116 and51107069)
文摘This paper is concerned with oscillatory behavior of a class of fourth-order delay dynamic equations on a time scale.In the general time scales case,four oscillation theorems are presented that can be used in cases where known results fail to apply.The results obtained can be applied to an equation which is referred to as Swift-Hohenberg delay equation on a time scale.These criteria improve a number of related contributions to the subject.Some illustrative examples are provided.
文摘In this paper, following a previous paper （[32] Permanence and extinction of a non- autonomous HIV-I model with two time delays, preprint） on the permanence and extinc- tion of a delayed non-autonomous HIV-1 within-host model, we introduce and investigate a delayed HIV-1 model including maximum homeostatic proliferation rate of CD4＋ T- cells and varying coefficients. By applying the asymptotic analysis theory and oscillation theory, we show： （i） the system will be permanent when the threshold value R. 〉 1, and for this case we also obtain the explicit estimate of the eventual lower bound of the HIV-1 virus load; （ii） the threshold value R＊ 〈 1 implies the extinction of the virus. Furthermore, we obtain that the threshold dynamics is in agreement with that of the corresponding autonomous system, which extends the classic results for the system with constant coefficients. Numerical simulations are also given to illustrate our main results, and in particular, some sensitivity test of R. is established.
文摘In this paper, we consider a Cohen-Grossberg neural network with three delays. Regard- ing time delays as a parameter, we investigate the effect of time delays on its dynamics. We show that there exist stability switches for time delays under certain conditions and the conditions for the existence of periodic oscillations are given by discussing the associated characteristic equation. Numerical simulations are given to illustrate the obtained results and interesting network behaviors are observed, such as multiple stability switches of the network equilibrium and synchronous （asynchronous） oscillations.
