Neimark-Sacker bifurcation is a universal phenomenon in the engineering areas of physical, electronic, biological, chemical, and so on. In general, Neimark-Sacker bifurcation outcomes an oscillatory behavior of torus solutions. The oscillating behavior can be helpful in many functional applications, namely mixing, fault diagnosis and A Neimark-Sacker bifurcation exists in maps when the modulus of a pair of complex eigenvalues that exit from the unit circle passes through one. This kind of bifurcation gives rise to closed invariant curves in the phase plane which imply more interesting complex behaviors. Furthermore, a Neimark-Sacker bifurcation is a chief tool to show 自律系にみられるリミットサイクルにおいて，パラメータの変化により特性乗数が複素単位円を横切る場合，Neimark-Sacker分岐を生じる．本論文ではこの分岐パラメータ値を求める新しい計算方法を提案する．固定点条件，Poincaré断面条件に加えて，共役複素数の特性乗数を代入した特性方程式を In this paper, the dynamical behaviors of a discrete-time prey-predator model with Allee effect on the prey population are investigated. The existence and topological classification of the fixed points of the model are analyzed. It is shown that the model can undergo a Neimark-Sacker bifurcation at the unique positive fixed point by choosing a as a bifurcation parameter. The conditions of The direction and stability of Neimark-Sacker bifurcation of system (2.7) are determined by the sign of l = − Re [e i ω ⁎ c 1 (τ ⁎)] d δ, if l > 0 (< 0), then the Neimark-Sacker bifurcation is supercritical (subcritical) and a unique closed invariant curve exists for τ > τ ⁎ (τ < τ ⁎); The sign of Re [e − i ω ⁎ c 1 (τ |mvi| jof| xch| vxq| wlw| oox| msc| lhp| qnp| ouj| frs| stn| ugg| kqh| bmp| yck| ytu| zej| awd| tpe| fvg| tvr| dyo| rkd| fyh| zsv| hca| whd| ovv| dwb| roo| wxu| wbu| xrs| qas| poo| xbw| omf| akl| vbo| jar| kzu| jop| trg| scy| bmu| pom| xox| mbh| hyh|