Differential Equations › Section B · First order differential equations › Topic B.8
Equilibrium solutions and stability
For an equation whose rate depends only on the current state, the constant solutions organise everything else. Find them, decide which attract and which repel, and you can predict the fate of every solution without solving the equation.
In this topic
- Autonomous equations
- The phase line
- Three kinds of equilibrium
- Worked example: a cubic
- The derivative test
- Worked example: a semi-stable equilibrium
- Reading long-run behaviour
- Bifurcations
- Common mistakes to avoid
- Key takeaways
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