论文标题
杂斜周期的稳定性：一种新方法
Stability of heteroclinic cycles: a new approach
论文作者
论文摘要
本文分析了在六个周期形成的三维流形中的杂斜网络中循环的稳定性，用于在游戏理论背景下开发的一个参数模型。我们显示了网络的渐近稳定性，该范围与内部平衡相兼容的一系列参数值，我们描述了一种渐近技术，以决定哪个循环（在网络中）在数字中可见。该技术包括将相关的动力学降低到合适的一维图，即所谓的\ emph {poxtive map}。投影图的固定点的稳定性决定了相关周期的稳定性。这种新的渐近方法的描述适用于更通用的网络类型，并且可能在计算动力学中有用。
This paper analyses the stability of cycles within a heteroclinic network lying in a three-dimensional manifold formed by six cycles, for a one-parameter model developed in the context of game theory. We show the asymptotic stability of the network for a range of parameter values compatible with the existence of an interior equilibrium and we describe an asymptotic technique to decide which cycle (within the network) is visible in numerics. The technique consists of reducing the relevant dynamics to a suitable one-dimensional map, the so called \emph{projective map}. Stability of the fixed points of the projective map determines the stability of the associated cycles. The description of this new asymptotic approach is applicable to more general types of networks and is potentially useful in computational dynamics.
