Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways.Chaotic behaviour in the sense of Marotto's definition is rigorously proven.A linear impulsive controller,which does not result in any change in one period-1 solution of the original system,is proposed to control and anti-control chaos.The numerical results for chaotic attractor,route leading to chaos,chaos control,and chaos anti-control,which are illustrated with two examples,are in good agreement with the theoretical analysis.
A ratio-dependent predator-prey system with stage structure and time delays for both prey and predator is considered in this paper. Both the predator and prey have two stages,immature stage and mature stage,and the growth of them is of Lotka-Volterra nature. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age,and that mature predators attack immature prey only. The global stability of three nonnegative equilibria and permanence are presented.
Lu Zhiqi,Wang Jiaoyan(Dept. of Math.,Henan Normal University,Xinxiang 453007,Henan)
