https://www.chenk.top/en/tags/lyapunov-exponents/Recent content in Lyapunov Exponents on Chen Kai BlogHugoenTue, 14 Nov 2023 09:00:00 +0000https://www.chenk.top/en/ode/09-bifurcation-chaos/Tue, 14 Nov 2023 09:00:00 +0000https://www.chenk.top/en/ode/09-bifurcation-chaos/<p><strong>In 1961, Edward Lorenz restarted a weather simulation from a rounded-off number — 0.506 instead of 0.506127.</strong> Within simulated weeks the forecast was unrecognisable. That single accident gave us <strong>the butterfly effect</strong> and turned chaos from a metaphor into a science. The lesson is profound and sober: equations that are <em>exactly</em> deterministic can still be <em>practically</em> unpredictable.</p> <p><figure class="article-figure"> <img src="https://blog-pic-ck.oss-cn-beijing.aliyuncs.com/posts/en/ode/09-bifurcation-chaos/illustration_1.png" alt="Ordinary Differential Equations (9): Chaos Theory and the Lorenz System — Chapter overview" loading="lazy" decoding="async" class="content-image"> </figure> </p>