Christophe LETELLIER
12/04/2017

There are many versions for the ``van der Pol’’ equation. Among them, there is this one, involving the cubic term, which reads

and which was investigated in details in [1]. This is sstem is a semi-conservative system which means that there is a continuum of attractors, that is, many many different attractors co-exist in the state space [2]. When parameter values are , , and , and initial conditions are

there is a toroidal chaotic attractor as shown in Fig. 1.

**Fig. 1. Toroidal chaotic attractor produced by the driven van der Pol equation.**

[1] **C. Letellier, V. Messager & R. Gilmore**, From quasi-periodicity to toroidal chaos : analogy between the Curry-Yorke map and the van der Pol system, *Physical Review E*, **77** (4), 046203, 2008.

[2] **O. Ménard, C. Letellier, J. Maquet, L. Le Sceller & G. Gouesbet**, Analysis of a non synchronized sinusoidally driven dynamical system, *International Journal of Bifurcation & Chaos*, **10** (7), 1759-1772, 2000.