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## Catastrophic Outbreak

I am enjoying Steven Strogatz second edition of “Non-linear Dynamics and Chaos”.

This post is motivated by this. The following gif relates to the model for insect outbreak. It shows the critical point parameter surface.

The differential equation: $\dot{x}=r x (1-\frac{x}{k})-\frac{x^2}{1+x^2}$. Note the  fixed point $x^*=0$ is  unstable.

Not as nice and smooth as I’d like but fun nonetheless.