“Period three to period two” bifurcation for piecewise linear models

Period Adding in Piecewise Linear Maps with Two Discontinuities

In this work we consider the border collision bifurcations occurring in a one-dimensional piecewise linear map with two discontinuity points. The map, motivated by an economic application, is written in a generic form and considered in the stable regime, with all slopes between zero and one. We prove that the period adding structures occur in maps with more than one discontinuity points and tha...

Lower bounds for two-period grooming via linear programming duality

In a problem arising in grooming for two-period optical networks, it is required to decompose the complete graph on n vertices into subgraphs each containing at most C edges, so that the induced subgraphs on a specified set of v ≤ n vertices each contain at most C ′ < C edges. The cost of the grooming is the sum, over all subgraphs, of the number of vertices of nonzero degree in the subgraph. T...

Influence of perturbations on period-doubling bifurcation.

Perturbed period-doubling bifurcation. I. Theory.

On a bifurcation structure mimicking period adding

In this work, we investigate a piecewise-linear discontinuous scalar map defined on three partitions. This map is specifically constructed in such a way that it shows a recently discovered bifurcation scenario in its pure form. Owing to its structure on the one hand and the similarities to the nested period-adding scenario on the other hand, we denoted the new bifurcation scenario as nested per...