Chaotic effects can arise from Eq. (1) if two conditions are
satisfied. First, at least one of the functions 
must contain a
nonlinear term (e.g., 
, 
, 
).
Second, there is a theorem [1]
which states that chaos only occurs in
Eq. (1) if 
.
For example, the famous Lorenz equations are given by
[1,2]
where 
, r, and b are all constants. Note the nonlinear
terms
and 
in the second and third equations, respectively, of
Eq. (5). For 
, 
, and r=28, one finds
that the system of equations in (5) gives rise to the so-called
Lorenz attractor [1,2]
(a ``strange attractor''), which in 1963 was historically
the first evidence of chaos in a dissipative system.
(Shortly before 1900, Henri Poincaré discovered chaos in a conservative
system.)
