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.)