What is a minimal, explicit dynamical system (as in, a series of coupled ordinary differential equations) that exhibits quasiperiodic oscillations for some region of parameter space? Two coupled Van der Pol oscillators have this property, for example; however I am hoping to find a dynamical system with a simpler form.
I am imagining something like a system of three variables, in which trajectories trace a spiral on a torus in three dimensional space.
A minimum, if boring example is that of two uncoupled 1D linear ODE (with incommensurate constants) on a torus, such as can be found in Hasselblatt & Katok:
$$\left\{ \begin{aligned} \dot x &= \omega_1\\ \dot y &= \omega_2, \end{aligned} \right. \tag{4.2.3} $$
whose trivial solution is
$$\left\{ \begin{aligned} x &= x_0 + \omega_1t\\ y &= y_0 + \omega_2t. \end{aligned} \right. \tag{4.2.4} $$
The simplest nontrivial example I could find is the forced van der Pol oscillator (still simpler than the example of two of them coupled, mentioned in the OP), found, e.g., in Guckenheimer's 1980 paper (e-print):
$$\left\{ \begin{aligned} \dot x &= y - \epsilon(x^3/3 -x)\\ \dot y &= -x+b\cos(\omega t), \end{aligned} \right. $$
which can be written as an autonomous system in 3D:
$$\left\{ \begin{aligned} \dot x &= y - \epsilon(x^3/3 -x)\\ \dot y &= -x + b\cos z\\ \dot z &= \omega. \end{aligned} \right. $$
A numerically integrated quasiperiodic trajectory of this system, in normalized variables, can be found in this paper (e-print):
