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300s School/ME 2016 - Nonlinear Dynamical Systems 1/2024-09-16.md
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# Systems in the Plane
Why do we care about looking at systems in the plane?
Well - we want to know about equilibrium points and how the system behaves around them.
Recall that equilibrium points are fixed. P = Q = 0
## Some Loose definitions
| Name | Definition |
| ------------- | ---------------------------------------------------------------------------------------------------- |
| Periodic | A trajectory loops upon itself |
| Stable | Trajectories converge to a point |
| Unstable | Trajectories diverge from a point |
| Linear Center | An equilibrium point that has orbits around it |
| Limit Cycle | Happens a lot with nonlinear systems. Trajectories are pulled some target trajectory and stay there. |
**Documentation**
- [<] ME2016 Week 3 Class ⏳ 2024-09-16