The Halvorsen system is a cyclically symmetric quadratic dynamical system given by
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
is a real parameter (Sprott 2010, pp. 83-85). The variables 
, 
, and 
depend on time, and primes denote derivatives
with respect to 
. Cycling the coordinates leaves
the system unchanged. On the invariant line 
, it reduces to 
. The equilibrium
point 
on this line is accompanied by a second one at 
when 
. The divergence
is 
, so for 
the flow contracts volume in
phase space. Sprott (2010, pp. 83-85) gives a
numerical example of a strange attractor for
.
