论文标题
D-Concave非自主标量的普通微分方程中吸引子和最小集的分叉理论
Bifurcation Theory of Attractors and Minimal Sets in D-Concave Nonautonomous Scalar Ordinary Differential Equations
论文作者
论文摘要
分析了标量非自主普通微分方程的两个单参数分叉问题，假设确定方程的时间依赖性函数的强制性以及其在状态变量方面的衍生物的凹陷。扭曲的形式主义导致对最小集合的数量和特性的分析以及全球吸引子的形状，其突然的变化决定了局部鞍节点，局部跨批评和全球干草叉分叉点的发生，最小值集和全球吸引者的不连续点的发生。
Two one-parametric bifurcation problems for scalar nonautonomous ordinary differential equations are analyzed assuming the coercivity of the time-dependent function determining the equation and the concavity of its derivative with respect to the state variable. The skewproduct formalism leads to the analysis of the number and properties of the minimal sets and of the shape of the global attractor, whose abrupt variations determine the occurrence of local saddle-node, local transcritical and global pitchfork bifurcation points of minimal sets and of discontinuity points of the global attractor.
