This paper presents an investigation on the phenomenon of delayed bifurcation in time-delayed slow-fast differential systems.Here the two delayed's have different meanings.The delayed bifurcation means that the bi...This paper presents an investigation on the phenomenon of delayed bifurcation in time-delayed slow-fast differential systems.Here the two delayed's have different meanings.The delayed bifurcation means that the bifurcation does not happen immediately at the bifurcation point as the bifurcation parameter passes through some bifurcation point,but at some other point which is above the bifurcation point by an obvious distance.In a time-delayed system,the evolution of the system depends not only on the present state but also on past states.In this paper,the time-delayed slow-fast system is firstly simplified to a slow-fast system without time delay by means of the center manifold reduction,and then the so-called entry-exit function is defined to characterize the delayed bifurcation on the basis of Neishtadt's theory.It shows that delayed Hopf bifurcation exists in time-delayed slow-fast systems,and the theoretical prediction on the exit-point is in good agreement with the numerical calculation,as illustrated in the two illustrative examples.展开更多
In this paper, we consider a unidirectional highway road with one entry/exit uniformly distributed on the road interval. One road side unit (RSU) is located on the position of the entry/exit. We build an analytical mo...In this paper, we consider a unidirectional highway road with one entry/exit uniformly distributed on the road interval. One road side unit (RSU) is located on the position of the entry/exit. We build an analytical model to study the network connectivity problem. In building the analytical model, we take into account several parameters, such as vehicle arrival rate, vehicle moving speed, vehicle communication radius, RSU communication radius, highway road length and the probability of vehicles driving through the entry/exit. The analytical model is verified by using simulation tools.展开更多
基金supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No.200430)in part by the National Natural Science Foundation of China (Grant Nos.10825207,10532050)
文摘This paper presents an investigation on the phenomenon of delayed bifurcation in time-delayed slow-fast differential systems.Here the two delayed's have different meanings.The delayed bifurcation means that the bifurcation does not happen immediately at the bifurcation point as the bifurcation parameter passes through some bifurcation point,but at some other point which is above the bifurcation point by an obvious distance.In a time-delayed system,the evolution of the system depends not only on the present state but also on past states.In this paper,the time-delayed slow-fast system is firstly simplified to a slow-fast system without time delay by means of the center manifold reduction,and then the so-called entry-exit function is defined to characterize the delayed bifurcation on the basis of Neishtadt's theory.It shows that delayed Hopf bifurcation exists in time-delayed slow-fast systems,and the theoretical prediction on the exit-point is in good agreement with the numerical calculation,as illustrated in the two illustrative examples.
文摘In this paper, we consider a unidirectional highway road with one entry/exit uniformly distributed on the road interval. One road side unit (RSU) is located on the position of the entry/exit. We build an analytical model to study the network connectivity problem. In building the analytical model, we take into account several parameters, such as vehicle arrival rate, vehicle moving speed, vehicle communication radius, RSU communication radius, highway road length and the probability of vehicles driving through the entry/exit. The analytical model is verified by using simulation tools.
