论文标题
d-concave非自主标量普通平差方程中的普通干草叉分叉
Generalized Pitchfork Bifurcations in D-Concave Nonautonomous Scalar Ordinary Differential Equations
论文作者
论文摘要
耗散量表非自主的普通微分方程$ x'= f（t，x）$的全球分叉图（$+λx$和$+λx$和$+λx^2 $）的全球分叉图描述了$ f $在$ t $中是$ t $ conterrents conterrents，并且是$ x $ x $ x $，描述了$ f $ conterrent conty $ x $，描述了$ f $ conterrents $ t $ x $。使用偏斜形式主义的使用使我们能够识别出随着最小设置数量和全球吸引子形状的变化而变化的分叉。在扰动$+λx$的情况下，可能会出现所谓的全球普遍的干草叉分叉，并且在自动动力学中缺乏类似物的特殊性。在这项工作中，对这种新的分叉模式进行了广泛的研究。
The global bifurcation diagrams for two different one-parametric perturbations ($+λx$ and $+λx^2$) of a dissipative scalar nonautonomous ordinary differential equation $x'=f(t,x)$ are described assuming that 0 is a constant solution, that $f$ is recurrent in $t$, and that its first derivative with respect to $x$ is a strictly concave function. The use of the skewproduct formalism allows us to identify bifurcations with changes in the number of minimal sets and in the shape of the global attractor. In the case of perturbation $+λx$, a so-called global generalized pitchfork bifurcation may arise, with the particularity of lack of an analogue in autonomous dynamics. This new bifurcation pattern is extensively investigated in this work.
