连续分段线性逼近下非线性常微分方程的吸引性和稳定性
Attraction and Stability of Nonlinear Ode's using Continuous Piecewise Linear Approximations
摘要：
本文给出了非线性常微分方程的吸引性和全局渐近稳定性的几个结果。主要结果是非常简单的应用产生的充分条件下，平衡点（假设一个唯一的平衡）是吸引的，也提供了各种选择，其中经典的线性化和其他现有的结果是本文的主要定理的特殊情况，包括著名的Markus-Yamabe猜想的推广。几个应用实例，以分析所提出的结果的优点和缺点，并比较这些结果与现有的成功的技术分析，在文献中提供。
英文摘要：
In this paper, several results concerning attraction and asymptotic stability in the large of nonlinear ordinary differential equations are presented. The main result is very simple to apply yielding a sufficient condition under which the equilibrium point (assuming a unique equilibrium) is attractive and also provides a variety of options among them the classical linearization and other existing results are special cases of the this main theorem in this paper including and extension of the well known Markus-Yamabe conjecture. Several application examples are presented in order to analyze the advantages and drawbacks of the proposed result and to compare such results with successful existing techniques for analysis available in the literature nowadays.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
