Period-incrementing, sausage-string-like structures, and multistability in a power converter with hysteresis control: An archetypal map approach

In this work, we investigate a one-dimensional discontinuous map with non-monotonic branches that models the dynamics of an H-bridge DC–AC converter with three-level hysteresis control. The applied control strategy results in a complex model defined by several implicit equations. The model exhibits an unusual bifurcation structure characterized by overlapping chains of regions associated with attracting cycles of the same period, resembling sausage-string-like components well known in period-adding bifurcation structures. However, the overall bifurcation structure in the considered model is not period-adding but period-incrementing, for which such sausage-string-like components have not been reported before. To gain insight into the organizing principles of this bifurcation structure, we developed a simplified archetypal map that captures the key properties and parameter dependencies of the original system. One of these properties is a certain symmetry which crucially influences the bifurcation structure. In particular, the structure is formed by double border collision bifurcations where two points of the involved cycles collide with boundaries in the state space. Additionally, our analysis reveals that the structure includes regions of multistability, where up to four attracting cycles coexist. Numerical evidence confirms that the archetypal map successfully replicates the bifurcation behavior observed in the original system.