一类非自治广义 Birkhoff 系统的稳定性和分岔
Stability and Bifurcation for a Type of Non-autonomous Generalized Birkhoffian Systems

摘要 研究一类非自治广义Birkhoff 系统的分岔。将该系统转化为梯度系统, 利用梯度系统的性质研究这一类系统平衡点的稳定性。研究表明, 当系统含有某个参数时, 系统平衡点的数目和稳定性将会随参数的变化而发生改变, 从而产生分岔现象。
Abstract Bifurcation for a type of non-autonomous generalized Birkhoffian systems is studied. Gradient representations for this type of non-autonomous generalized Birkhoffian systems are given. The stability of equilibrium point of these systems is discussed by the characteristic of the gradient system. Further the systems which contain some parameter are studied. The stability and the number of equilibrium point will change along with the change of the parameter to produce the bifurcation phenomenon.