Perturbations of a Spatial Ricker Model: Break of Chaos.

It is well known that as the intrinsic growth rate r increases, the Ricker map exhibits an irreversible period doubling route to chaos. If a constant positive perturbation is introduced, then there is a break of chaos giving birth to a two-cycle. We study a similar effect in a 2-dimensional spatial setting where each cell of the lattice is influenced by its nearest neighbours only. Chaos is not observed for r large enough, and the model can incorporate cells that experience two-cycle oscillations with stable dynamics at some locations. A Ricker map with a negative perturbation (depletion) is discussed, as well as some generalizations of the problem. [ABSTRACT FROM AUTHOR]