Detecting Bifurcation Types and Characterizing Stability in DC–DC Switching Converters by Duplicate Symbolic Sequence and Weight Complexity

Based on the characteristics of dc-dc switching converters and the logical arithmetic method of computer that changes to decimal system from binary system, the main switching block is presented to distinguish the switching behaviors and the degree of the converter´s complexity during one switching period. The main symbolic sequence is established to clearly show how the switching modes change in one switching period. Adopting the coarse-grained symbolic sequence method, the secondary switching block and secondary symbolic sequence are established in terms of main switching block too. Hence, the duplicate symbolic sequence is put forward to detect bifurcation types in dc-dc switching converters. Based on the duplicate symbolic sequence, the concept of weight complexity is first defined and utilized to analyze border collision and bifurcation phenomena qualitatively along with Lempel-Ziv (L-Z) complexity. The presented weight complexity and the L-Z complexity are combined to introduce the stability index for guiding circuit design of power electronics. Finally, voltage-mode-controlled flyback converter is used as an example to illustrate the applications of the proposed duplicate symbolic sequence and complexity to detect bifurcation behaviors of the switching system.