科技回声

A lot of people don't get further than Malthus, and don't realize that he was just the first pioneer. They think "Malthus was wrong", and don't realize the rabbit hole that opens up once you start treating population dynamics mathematically.

Volterra also contributed to materials science, more precisely with dislocations in crystals. Always amaze me how people in the past could make huge impact in totally different fields.

A long time ago I wrote code to run a visual simulation that combines flocking behavior with Lotka-Volterra dynamics<p><a href="https://www.youtube.com/watch?v=-_JWAh0lP8Q" rel="nofollow">https://www.youtube.com/watch?v=-_JWAh0lP8Q</a><p>It's a stochastic simulation (no differential equations), but it produces predator-prey population swings that are pretty close to the Lotka-Volterra model

Lotka–Volterra equations -> Logistic function -> Logistic map -> Mandelbrot set for an interesting connection that might not be immediately apparent. The concepts all turn up around the same time once the line of inquiry becomes chaotic recursive systems.

For those interested in this stuff, I strongly recommend Strogatz "Nonlinear dynamics and chaos".

Volterra also contributed to materials science, more precisely with dislocations in crystals. Always amaze me how people in the past could make huge impact in totally different fields.

For those interested in this stuff, I strongly recommend Strogatz "Nonlinear dynamics and chaos".

Lotka–Volterra Equations

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Lotka–Volterra Equations

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