In this paper, we study the step criteria of numerical methods for delay differential equations, some results on step-length for Range - Kutta methods and linear multistep methods are given.
O437 95010336光学双稳态离散模型的动力学行为=The dynamicbehavior of a discrete model of opticalbistable system[刊,中]/杨援,戴建华,张洪钧(中科院北京物理所)//物理学报.—1994,43(5).—699—706对描写光学双稳系统的延时微分...O437 95010336光学双稳态离散模型的动力学行为=The dynamicbehavior of a discrete model of opticalbistable system[刊,中]/杨援,戴建华,张洪钧(中科院北京物理所)//物理学报.—1994,43(5).—699—706对描写光学双稳系统的延时微分方程作了离散化处理,在N=1的情况下,得到一个二维迭代方程,研究结果表明:系统刚失稳时不是单模振荡,而是四模同时振荡。展开更多
A dynamic model of schistosoma japonicum transmission is presented that incorporates effects of the prepatent periods of the different stages of schistosoma into Baxbour＇s model. The model consists of four delay diff...A dynamic model of schistosoma japonicum transmission is presented that incorporates effects of the prepatent periods of the different stages of schistosoma into Baxbour＇s model. The model consists of four delay differential equations. Stability of the disease free equilibrium and the existence of an endemic equilibrium for this model are stated in terms of a key threshold parameter. The study of dynamics for the model shows that the endemic equilibrium is globally stable in an open region if it exists and there is no delays, and for some nonzero delays the endemic equilibrium undergoes Hopf bifurcation and a periodic orbit emerges. Some numerical results are provided to support the theoretic results in this paper. These results suggest that prepatent periods in infection affect the prevalence of schistosomiasis, and it is an effective strategy on schistosomiasis control to lengthen in prepatent period on infected definitive hosts by drug treatment （or lengthen in prepatent period on infected intermediate snails by lower water temperature）.展开更多
In this paper, a class of delay differential equations with nonlinear impulsive control is discussed. Based on the nonsmooth analysis, criteria of stability are obtained for delay differential equations with nonlinear...In this paper, a class of delay differential equations with nonlinear impulsive control is discussed. Based on the nonsmooth analysis, criteria of stability are obtained for delay differential equations with nonlinear impulses control under certain conditions. These criteria can be applied to some neural network models. At the end of the paper, two examples are provided to illustrate the feasibility and effectiveness of the proposed results.展开更多
A differential-algebraic prey--predator model with time delay and Allee effect on the growth of the prey population is investigated. Using differential-algebraic system theory, we transform the prey predator model int...A differential-algebraic prey--predator model with time delay and Allee effect on the growth of the prey population is investigated. Using differential-algebraic system theory, we transform the prey predator model into its normal form and study its dynamics in terms of local analysis and Hopf bifurcation. By analyzing the associated characteristic equation, it is observed that the model undergoes a Hopf bifurcation at some critical value of time delay. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions, and an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included.展开更多
基金the National Nature Science Foundation(10171067)Shanghai Municipal Education Commission(No.04DB07)the Special Funds for Major Specialties of Shanghai Education Committee.
文摘In this paper, we study the step criteria of numerical methods for delay differential equations, some results on step-length for Range - Kutta methods and linear multistep methods are given.
基金E-Institutes of Shanghai Municipal Education Commission (E03004)Shanghai Municipal Education Commission (04DB07, 07ZZ64)+1 种基金Shanghai Science and Technology Committee (03QA14036)The Special Funds for Major Specialties of Shanghai Education Committee NSFC(1067130)
文摘O437 95010336光学双稳态离散模型的动力学行为=The dynamicbehavior of a discrete model of opticalbistable system[刊,中]/杨援,戴建华,张洪钧(中科院北京物理所)//物理学报.—1994,43(5).—699—706对描写光学双稳系统的延时微分方程作了离散化处理,在N=1的情况下,得到一个二维迭代方程,研究结果表明:系统刚失稳时不是单模振荡,而是四模同时振荡。
基金supported by the National Natural Science Foundation of China(Nos.10831003,10925102)the Program of Shanghai Subject Chief Scientist(No.10XD1406200)
文摘A dynamic model of schistosoma japonicum transmission is presented that incorporates effects of the prepatent periods of the different stages of schistosoma into Baxbour＇s model. The model consists of four delay differential equations. Stability of the disease free equilibrium and the existence of an endemic equilibrium for this model are stated in terms of a key threshold parameter. The study of dynamics for the model shows that the endemic equilibrium is globally stable in an open region if it exists and there is no delays, and for some nonzero delays the endemic equilibrium undergoes Hopf bifurcation and a periodic orbit emerges. Some numerical results are provided to support the theoretic results in this paper. These results suggest that prepatent periods in infection affect the prevalence of schistosomiasis, and it is an effective strategy on schistosomiasis control to lengthen in prepatent period on infected definitive hosts by drug treatment （or lengthen in prepatent period on infected intermediate snails by lower water temperature）.
基金supported by Natural Science Foundation of China under Grant Nos.10972018 and 11072013
文摘In this paper, a class of delay differential equations with nonlinear impulsive control is discussed. Based on the nonsmooth analysis, criteria of stability are obtained for delay differential equations with nonlinear impulses control under certain conditions. These criteria can be applied to some neural network models. At the end of the paper, two examples are provided to illustrate the feasibility and effectiveness of the proposed results.
基金This work was supported by National Science Foundation of China 61273008 and 61203001, Doctor Startup Fund of Liaoning Province （20131026）, Fundamental Research Funds for the Central University （N140504005） and China Scholarship Council. The authors gratefully thank referees for their valuable suggestions.
文摘A differential-algebraic prey--predator model with time delay and Allee effect on the growth of the prey population is investigated. Using differential-algebraic system theory, we transform the prey predator model into its normal form and study its dynamics in terms of local analysis and Hopf bifurcation. By analyzing the associated characteristic equation, it is observed that the model undergoes a Hopf bifurcation at some critical value of time delay. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions, and an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included.
