This paper is concerned with a delay differential equationx=-x + f(y(t-r)), y=-y-f(x(t-r)),where delay r is a positive constant, and f is a signal transmission function of McCulloch-Pitts type.We obtain some sufficien...This paper is concerned with a delay differential equationx=-x + f(y(t-r)), y=-y-f(x(t-r)),where delay r is a positive constant, and f is a signal transmission function of McCulloch-Pitts type.We obtain some sufficient and necessary conditions for the asymptotic behavior of network (*) with σ ≤-1 .The results obtained show that the large time behaviors of solutions of (*) are dependent of r if σ= -1. These results improve the corresponding theorems in [3] by removing the restriction of the initial conditions.展开更多
In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Liénard-type equation with delays.
Considering the immune response and intracellular delay, we propose a two-strain virus model and investigate dynamics of this mathematical model. The global dynamics of the model are completely determined by introduci...Considering the immune response and intracellular delay, we propose a two-strain virus model and investigate dynamics of this mathematical model. The global dynamics of the model are completely determined by introducing suitable Lyapunov functionals. We show that if the basic reproduction number is less than one, then both strains die out; but when the number is greater than one, at least one of the strains become endemic depending on the parameter values. The theoretical results provide some useful information on the dynamics of the two strains virus.展开更多
This paper is concerned with a delay difference system. Some interesting results are obtained for the asymptotic behaviors of the system. Our theorems improve the corresponding theorems in the relevant literature by r...This paper is concerned with a delay difference system. Some interesting results are obtained for the asymptotic behaviors of the system. Our theorems improve the corresponding theorems in the relevant literature by removing the restriction of the initial conditions.展开更多
文摘This paper is concerned with a delay differential equationx=-x + f(y(t-r)), y=-y-f(x(t-r)),where delay r is a positive constant, and f is a signal transmission function of McCulloch-Pitts type.We obtain some sufficient and necessary conditions for the asymptotic behavior of network (*) with σ ≤-1 .The results obtained show that the large time behaviors of solutions of (*) are dependent of r if σ= -1. These results improve the corresponding theorems in [3] by removing the restriction of the initial conditions.
基金This work was supported by the NNSF of China (10071016) the Doctor Program Foundation of the Ministry of Education of China (20010532002) the Key Project of Chinese Ministry of Education (No.[2002]78).
文摘In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Liénard-type equation with delays.
基金supported by Scientific Research Fund of Hunan Provincial Education Department(13K012)National Natural Science Foundation of China(61102035)
文摘Considering the immune response and intracellular delay, we propose a two-strain virus model and investigate dynamics of this mathematical model. The global dynamics of the model are completely determined by introducing suitable Lyapunov functionals. We show that if the basic reproduction number is less than one, then both strains die out; but when the number is greater than one, at least one of the strains become endemic depending on the parameter values. The theoretical results provide some useful information on the dynamics of the two strains virus.
基金Project supported by NNSF of China (No. 10271044).
文摘This paper is concerned with a delay difference system. Some interesting results are obtained for the asymptotic behaviors of the system. Our theorems improve the corresponding theorems in the relevant literature by removing the restriction of the initial conditions.
