Recommendation for dynamical system with complex behaviors

Question

I want to learn the behaviors of dynamical systems, especially the in form of $X'=f(X)$ and $X'=f(t,X)$ in $\mathbb{R}^3$.

I know Lorentz system is such a system(typically $\sigma=10,\beta=\frac{8}{3},\rho=28$).

\begin{array}{rcl} \dot x &=& \sigma(y-x) \\ \dot y &=& \rho x-y-xz \\ \dot z &=& -\beta z+xy \end{array}

Any other one which is famous or complex enough?

Answer 1

The Lorenz system is famous for having a strange attractor despite being given by simple equations.

Other famous strange attractors also given by simple equations include the Rössler attractor and Chua's attractor.