Fractional linear maps have played a key role in mathematical biology,population dynamics,and other research areas.In this paper,a special kind of Ricatti map is studied in detail in order to determine the asymptotica...Fractional linear maps have played a key role in mathematical biology,population dynamics,and other research areas.In this paper,a special kind of Ricatti map is studied in detail in order to determine the asymptotical behaviors of fixed points and periodic solutions.Making use of composition operation of maps and the methods of dynamical systems and qualitative theory,fixed points or periodic orbits are expressed precisely,average value of periodic solution is estimated concretely,and several different bounds are obtained for periodic solutions of the Beverton⁃Holt map when both intrinsic growth rate and carrying capacity change periodically.In addition,some sufficient conditions are given about the attenuation of periodic solution of the non⁃autonomous Beverton⁃Holt equation.Compared with present works in literature,our results about bounds of periodic solutions are more precise,and our proofs about the attenuation of periodic solution are more concise.展开更多
文摘Fractional linear maps have played a key role in mathematical biology,population dynamics,and other research areas.In this paper,a special kind of Ricatti map is studied in detail in order to determine the asymptotical behaviors of fixed points and periodic solutions.Making use of composition operation of maps and the methods of dynamical systems and qualitative theory,fixed points or periodic orbits are expressed precisely,average value of periodic solution is estimated concretely,and several different bounds are obtained for periodic solutions of the Beverton⁃Holt map when both intrinsic growth rate and carrying capacity change periodically.In addition,some sufficient conditions are given about the attenuation of periodic solution of the non⁃autonomous Beverton⁃Holt equation.Compared with present works in literature,our results about bounds of periodic solutions are more precise,and our proofs about the attenuation of periodic solution are more concise.
