# Dictionary of Mathematical Eponymy: The Ueda Attractor

### What is a Ueda Attractor?

It looks like this. Pretty, huh?

It’s a phase solution of the Duffing equation $\ddot x + 0.05 \dot x + x^3 = 7.5\cos(t)$. It is a *strange attractor* – it is not periodic, but it is dense (and nearby trajectories converge into it).

### Why is it interesting?

I know I said in the last post that fluid dynamics is always interesting, but chaos theory knocks FD into a trumpet of infinite surface area.

I love chaos theory’s origin story (the whole Lorenz/butterfly affair, one of the stories my Uncle Bill told me that set me on a mathematical course). The thing is, I’m not certain Lorenz got there first.

It’s a bit hard to pin down the birthdate of the butterfly – I haven’t got any better than “the winter of 1961” and a suggestion that this means the winter *at the end* of 1961; Ueda recorded the output of a numerical simulation with chaotic solution in late November 1961. His plot is kept at the Brookhaven National Laboratory in the US, and is regarded as the oldest existing chaotic data.

### Who is Yoshisuke Ueda?

Yoshisuke Ueda was born in Kobe, Japan in 1936. He studied at Kyoto University, gaining a Bachelor’s degree in 1959, a Master’s in 1961 and a PhD in 1965. He became a full professor in 1985.

(Reference: Kehui Sun, A Di-li Duo Li-kun, Yanqing Dong, Huihai Wang, and Ke Zhong; *Multiple Coexisting Attractors and Hysteresis in
the Generalized Ueda Oscillator*; Mathematical Problems in Engineering 2013. http://dx.doi.org/10.1155/2013/256092)

* Edited 2022-10-10 to add missing image and reference thereto. Thanks, Andrew!