This paper investigates the global behavior of controlled dynamical agents in directed networks. The agents are Lyapunov stable, are distributed in a line, and communicate through a directed network. The communication...This paper investigates the global behavior of controlled dynamical agents in directed networks. The agents are Lyapunov stable, are distributed in a line, and communicate through a directed network. The communication topology of the network is characterized by a directed graph and the control protocol is designed in simple linear decentralized feedback law. We study the different conditions under which agents will achieve aggregation, and critical and divergent trajectories, respectively. Our investigation on the dynamical agent system under network is extended to the time-delay network case. Furthermore, we study the case with two pre-specified virtual leaders in the system. Numerical simulations are given and demonstrate that our theoretical results are effective.展开更多
This study considers SEIVR epidemic model with generalized nonlinear saturated inci- dence rate in the host population horizontally to estimate local and global equilibriums. By using the Rout^Hurwitz criteria, it is ...This study considers SEIVR epidemic model with generalized nonlinear saturated inci- dence rate in the host population horizontally to estimate local and global equilibriums. By using the Rout^Hurwitz criteria, it is shown that if the basic reproduction number R0 〈 1, the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if R0 〈 1. The geometric approach is used to present the global stability of the endemic equilibrium. For R0〉 1, the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.展开更多
基金supported by the National Natural Science Foundation of China (No.60674046)
文摘This paper investigates the global behavior of controlled dynamical agents in directed networks. The agents are Lyapunov stable, are distributed in a line, and communicate through a directed network. The communication topology of the network is characterized by a directed graph and the control protocol is designed in simple linear decentralized feedback law. We study the different conditions under which agents will achieve aggregation, and critical and divergent trajectories, respectively. Our investigation on the dynamical agent system under network is extended to the time-delay network case. Furthermore, we study the case with two pre-specified virtual leaders in the system. Numerical simulations are given and demonstrate that our theoretical results are effective.
文摘This study considers SEIVR epidemic model with generalized nonlinear saturated inci- dence rate in the host population horizontally to estimate local and global equilibriums. By using the Rout^Hurwitz criteria, it is shown that if the basic reproduction number R0 〈 1, the disease-free equilibrium is locally asymptotically stable. When the basic reproduction number exceeds the unity, then the endemic equilibrium exists and is stable locally asymptotically. The system is globally asymptotically stable about the disease-free equilibrium if R0 〈 1. The geometric approach is used to present the global stability of the endemic equilibrium. For R0〉 1, the endemic equilibrium is stable globally asymptotically. Finally, the numerical results are presented to justify the mathematical results.
