Bifurcations of an iterated mapping with retardations

An elementary example for an iterated mapping with retardation is defined, which exhibits a Whitney fold bifurcation of the long-time limit. The long-time dynamics is quite different from the bifurcation scenario known for conventional iterated mappings. There appear two nontrivial power-law exponents, one describing the decay toward a plateau value and the other describing the one below this plateau, which vary continuously with a model parameter. The slowing down of the dynamics near the critical point is ruled by two divergent time scales, characterized by two different nonuniversal exponents. This leads to a stretching of the relaxation over large time intervals. A scaling law description of the bifurcation dynamics is derived.