In this paper, a discretized SIR model with pulse vaccination and time delay is proposed. We introduce two thresholds R* and R<sub>*</sub>, and further prove that the disease-free periodic solution is glob...In this paper, a discretized SIR model with pulse vaccination and time delay is proposed. We introduce two thresholds R* and R<sub>*</sub>, and further prove that the disease-free periodic solution is globally attractive if R* is less than unit and the disease can invade if R<sub>*</sub> is larger than unit. The numerical simulations not only illustrate the validity of our main results, but also exhibit bifurcation phenomenon. Our result shows that decreasing infection rate can put off the disease outbreak and reduce the number of infected individuals.展开更多
Peer-to-Peer （P2P） botnet has emerged as one of the most serious threats to lnternet security. To effectively elimi- nate P2P botnet, a delayed SEIR model is proposed,which can portray the formation process of P2P b...Peer-to-Peer （P2P） botnet has emerged as one of the most serious threats to lnternet security. To effectively elimi- nate P2P botnet, a delayed SEIR model is proposed,which can portray the formation process of P2P botnet. Then, the local stability at equilibria is carefully analyzed by considering the eigenvalues＇ distributed ranges of characteristic equations. Both mathematical analysis and numerical simulations show that the dynamical features of the proposed model rely on the basic re- production number and time delay r. The results can help us to better understand the propagation behaviors of P2P botnet and design effective counter-botnet methods.展开更多
In this paper, we consider the discrete Hematopoiesis model with a time delay： x（n＋1）-x（n）=-r（n）x（n）＋a（n）/（1＋x^u（n-r）） Sufficient conditions for the existence of a unique uniformly asymptotically sta...In this paper, we consider the discrete Hematopoiesis model with a time delay： x（n＋1）-x（n）=-r（n）x（n）＋a（n）/（1＋x^u（n-r）） Sufficient conditions for the existence of a unique uniformly asymptotically stable positive almost periodic solution are obtained by the work of IS. N. Zhang, G. Zheng, Almost periodic solutions of delay difference systems, Appl. Math. Comput. 131 （2002） 497 516]. Some examples are considered to illustrate the main results.展开更多
The control of time delay systems is still an open area for research. This paper proposes an enhanced model predictive discrete-time sliding mode control with a new sliding function for a linear system with state dela...The control of time delay systems is still an open area for research. This paper proposes an enhanced model predictive discrete-time sliding mode control with a new sliding function for a linear system with state delay. Firstly, a new sliding function including a present value and a past value of the state, called dynamic surface, is designed by means of linear matrix inequalities （LMIs）. Then, using this dynamic function and the rolling optimization method in the predictive control strategy, a discrete predictive sliding mode controller is synthesized. This new strategy is proposed to eliminate the undesirable effect of the delay term in the closed loop system. Also, the designed control strategy is more robust, and has a chattering reduction property and a faster convergence of the system s state. Finally, a numerical example is given to illustrate the effectiveness of the proposed control.展开更多
文摘In this paper, a discretized SIR model with pulse vaccination and time delay is proposed. We introduce two thresholds R* and R<sub>*</sub>, and further prove that the disease-free periodic solution is globally attractive if R* is less than unit and the disease can invade if R<sub>*</sub> is larger than unit. The numerical simulations not only illustrate the validity of our main results, but also exhibit bifurcation phenomenon. Our result shows that decreasing infection rate can put off the disease outbreak and reduce the number of infected individuals.
基金National Natural Science Foundation of China(No.61379125)Program for Basic Research of Shanxi Province(No.2012011015-3)Higher School of Science and Technology Innovation Project of Shanxi Province(No.2013148)
文摘Peer-to-Peer （P2P） botnet has emerged as one of the most serious threats to lnternet security. To effectively elimi- nate P2P botnet, a delayed SEIR model is proposed,which can portray the formation process of P2P botnet. Then, the local stability at equilibria is carefully analyzed by considering the eigenvalues＇ distributed ranges of characteristic equations. Both mathematical analysis and numerical simulations show that the dynamical features of the proposed model rely on the basic re- production number and time delay r. The results can help us to better understand the propagation behaviors of P2P botnet and design effective counter-botnet methods.
文摘In this paper, we consider the discrete Hematopoiesis model with a time delay： x（n＋1）-x（n）=-r（n）x（n）＋a（n）/（1＋x^u（n-r）） Sufficient conditions for the existence of a unique uniformly asymptotically stable positive almost periodic solution are obtained by the work of IS. N. Zhang, G. Zheng, Almost periodic solutions of delay difference systems, Appl. Math. Comput. 131 （2002） 497 516]. Some examples are considered to illustrate the main results.
基金supported by Ministry of the Higher Education and Scientific Research in Tunisa
文摘The control of time delay systems is still an open area for research. This paper proposes an enhanced model predictive discrete-time sliding mode control with a new sliding function for a linear system with state delay. Firstly, a new sliding function including a present value and a past value of the state, called dynamic surface, is designed by means of linear matrix inequalities （LMIs）. Then, using this dynamic function and the rolling optimization method in the predictive control strategy, a discrete predictive sliding mode controller is synthesized. This new strategy is proposed to eliminate the undesirable effect of the delay term in the closed loop system. Also, the designed control strategy is more robust, and has a chattering reduction property and a faster convergence of the system s state. Finally, a numerical example is given to illustrate the effectiveness of the proposed control.
