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On delta-modulated control: A simple system with complex dynamics

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  • Xia, Xiaohua
  • Chen, Guanrong

Abstract

In this paper, we investigate some interesting properties of a scalar system controlled by Δ-modulated feedback. We show that there are three different cases. In the first case, there is a minimal global attractor which consists of only two points. The two points form either one 2-periodic orbit or two 1-periodic orbits (fixed points). We also characterize the attracting region for each of these two points. In the second case, the maximal stabilizable region is bounded, and there is a minimal local attractor inside this stabilizable region. In the third case, the maximal stabilizable set is a Cantor set, which is a repeller of the system, and the system is chaotic on the Cantor set.

Suggested Citation

  • Xia, Xiaohua & Chen, Guanrong, 2007. "On delta-modulated control: A simple system with complex dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1314-1328.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:4:p:1314-1328
    DOI: 10.1016/j.chaos.2006.01.092
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