Insect outbreak

Time scale separation

• population evolves on fast time scale

• trees on slow time scale

• $\dot{N} = NR(1 - \frac{N}{K}) - p(N)$

• $p(N)$ - predatory function

• $[r] = [k] = 1$ ⇆ means dimension is 1.

Stability diagram

• we forget about unstable fixed points

Flows on the circle

Non-uniform

• lowest point = most interesting because oscillator spends most time there → bottleneck

oscillations for $a < \omega$

• important!

Fireflies