论文标题
在Lyapunov稳定性定理的远期不变性时，局部稳定性
On forward invariance in Lyapunov stability theorem for local stability
论文作者
论文摘要
当使用Lyapunov稳定定理证明局部稳定性时，通常会忽略吸引吸引盆地的正向不变性；即使Lyapunov函数在平衡的邻域中单调降低，动态也可能从该社区逃脱。在本说明中，我们通过找到一个向前不变的较小社区来解决这一差距。这有助于我们在不跟踪每个解决方案路径的情况下更自然地证明局部稳定性。同样，我们证明了有关景点盆地的传统定理，而无需向前不变。 关键字：Lyapunov功能，局部稳定性，正向不变性，进化动力学。
Forward invariance of a basin of attraction is often overlooked when using a Lyapunov stability theorem to prove local stability; even if the Lyapunov function decreases monotonically in a neighborhood of an equilibrium, the dynamic may escape from this neighborhood. In this note, we fix this gap by finding a smaller neighborhood that is forward invariant. This helps us to prove local stability more naturally without tracking each solution path. Similarly, we prove a transitivity theorem about basins of attractions without requiring forward invariance. Keywords: Lyapunov function, local stability, forward invariance, evolutionary dynamics.
