This paper discusses a novel approach to obtaining mathematically rigorous results on the global dynamics of ordinary differential equations. We study switching models of regulatory networks. To each switching network we associate a Morse graph, a computable object that describes a Morse decomposition of the dynamics. In this paper we show that all smooth perturbations of the switching system share the same Morse graph and we compute explicit bounds on the size of the allowable perturbation. This shows that computationally tractable switching systems can be used to characterize dynamics of smooth systems with steep nonlinearities.

中文翻译：

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二维陡峭非线性的全局动力学。

本文讨论了一种获得常微分方程全局动力学数学严格结果的新方法。我们研究监管网络的切换模型。我们将每个交换网络关联一个莫尔斯图，这是一个描述动力学莫尔斯分解的可计算对象。在本文中，我们证明了切换系统的所有平滑扰动共享相同的莫尔斯图，并且我们计算了允许扰动大小的显式界限。这表明计算上易于处理的切换系统可用于表征具有陡峭非线性的平滑系统的动力学特征。