https://www.chenk.top/en/tags/bifurcation/Recent content in Bifurcation on Chen Kai BlogHugoenWed, 11 Oct 2023 09:00:00 +0000https://www.chenk.top/en/ode/07-systems-and-phase-plane/Wed, 11 Oct 2023 09:00:00 +0000https://www.chenk.top/en/ode/07-systems-and-phase-plane/<p><strong>A small push hits a system. Does it return to rest, drift away, or break entirely?</strong> That single question decides whether bridges survive storms, ecosystems recover from droughts, and economies bounce back from crises. Stability theory answers it — and it does so <em>without ever solving the differential equation</em>. We will learn to read the destiny of a system off the geometry of its phase plane.</p> <p><figure class="article-figure"> <img src="https://blog-pic-ck.oss-cn-beijing.aliyuncs.com/posts/en/ode/07-systems-and-phase-plane/illustration_1.png" alt="Ordinary Differential Equations (7): Stability Theory — Chapter overview" loading="lazy" decoding="async" class="content-image"> </figure> </p>