Differential Equations › Section E · Systems of differential equations › Topic E.11
Nonlinear systems: equilibria and linearization
Most nonlinear systems have no solution formula, yet close to each equilibrium they behave almost exactly like a linear system. Finding the equilibria and linearising there gives a reliable local picture of the whole phase plane.
In this topic
- Beyond linear systems
- Equilibria and nullclines
- The Jacobian and linearisation
- Classifying with trace and determinant
- When linearisation can be trusted
- Worked example: competing species
- Worked example: a damped pendulum
- A centre that does not survive
- Basins of attraction and separatrices
- Common mistakes to avoid
- Key takeaways
This topic is part of Wuanberri Pro. Checking your access…