Analytical study of funnel type Rössler attractor.

We investigate the behavior of a typical trajectory in a funnel type Rössler attractor. Using a suitable averaging method, we propose to describe the originally more difficult time-continuous chaotic behavior of the system using an approximate four-parameter surrogate iteration scheme. This approach has the merits of helping one see more easily how the height of the peaks and the peak-to-peak durations vary as one tunes the system parameters. Our analytical results compare favorably well with those obtained through the numerical integration of the system.