非线性微分方程中有限周期解的稳定性和灾难性行为

Tikrit Journal of Pure Science Pub Date : 2023-12-25 DOI:10.25130/tjps.v28i6.1382

Isam R. Faeq, Shwan O. Abdalrahman

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摘要

本研究侧重于非线性微分方程中有限周期解的稳定性和灾难行为。研究探讨了折叠面的出现及其与鞍节点分岔的关系，并将其分为折叠和蝴蝶类型的灾变。此外，还讨论了如何应用灾变理论分析解随系统参数变化而发生的质变。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Stability and Catastrophic Behavior of Finite Periodic Solutions in Non-Linear Differential Equations

This study focuses on the stability and catastrophic behavior of finite periodic solutions in non-linear differential equations. The occurrence of folding surfaces and their relationship with saddle-node bifurcations are explored, being classified as fold and butterfly types of catastrophes. Additionally, the application of catastrophe theory is discussed to analyze the qualitative changes in solutions with the change in system parameters.

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Tikrit Journal of Pure Science

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