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Date: 22-5-2018
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Date: 12-6-2018
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Given a system of two ordinary differential equations
(1) |
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(2) |
let and denote fixed points with , so
(3) |
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(4) |
Then expand about so
(5) |
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(6) |
To first-order, this gives
(7) |
where the matrix, or its generalization to higher dimension, is called the stability matrix. Analysis of the eigenvalues (and eigenvectors) of the stability matrix characterizes the type of fixed point.
REFERENCES:
Tabor, M. "Linear Stability Analysis." §1.4 in Chaos and Integrability in Nonlinear Dynamics: An Introduction. New York: Wiley, pp. 20-31, 1989.
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كيف تساهم الأطعمة فائقة المعالجة في تفاقم مرض يصيب الأمعاء؟
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مشروع ضخم لإنتاج الهيدروجين الأخضر يواجه تأخيرًا جديدًا
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المجمع العلمي يختتم دورته القرآنية في فن الصوت والنغم بالطريقة المصرية
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