A modified Ricker map and its bursting oscillations.

In our search to understand complex oscillation in discrete dynamic systems, we modify the Ricker map, where one parameter is also a dynamic variable. Using the bistable behavior of the fixed point solution, we analyze two response functions that characterize the change of the dynamic parameter. The 2D map sustains different types of burst oscillations that depend on the response functions. In either case, the parameter values yield a slow dynamic variable required to observe bursting-type oscillations.