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.
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