Self-similarity in the bifurcation structure involving period tripling, and a suggested generalization to period n-tupling

Abstract

We compute the bifurcation structure in the parameter space of the periodically forced Toda oscillator model of class B lasers. The substructures, born in the process of period tripling, appear in a self-similar manner within the main bifurcation structure. Next, our observations suggest that, similar to period tripling, the birth of an n-tupled saddlenode ( n = 4,5,…) around a given stable periodic orbit is also a generic phenomenon of this oscillator. These n-tupling processes create substructures as in the case of period tripling. Taking into account all such n-tupling processes, the composite bifurcation structure apparently exhibits a new self-similar feature.