  A new type of deterministic chaos for a system described by iterative
two-dimensional maps is reported. The series being generated by the original
map has an average upward trend while the first difference, which is the series
of changes from one period to the next, exhibits chaotic behavior through
period doubling bifurcation. Furthermore, step-wise time series appears as the
values of the bifurcation parameter are large, and the first difference of the
time series exhibits intermittent chaos.
