TY - JOUR
T1 - An improvement on Marotto's theorem and its applications to chaotification of switching systems
AU - Zhao, Yi
AU - Xie, Lingli
AU - Yiu, Ka Fai Cedric
PY - 2009/3/15
Y1 - 2009/3/15
N2 - The controversy surrounding the correctness of Marotto's theorem continues over the last two decades, with many researchers claiming to have found an error in the proof. In this paper, we show that Marotto's theorem is indeed correct for analyzing the existence of chaos in the sense of Li-Yorke even after relaxing certain assumptions in the proof. In addition, we extend the theory to derive the conditions for the existence of chaos in the sense of Devaney. We show that these results can be applied to study the chaotification of linear switching systems.
AB - The controversy surrounding the correctness of Marotto's theorem continues over the last two decades, with many researchers claiming to have found an error in the proof. In this paper, we show that Marotto's theorem is indeed correct for analyzing the existence of chaos in the sense of Li-Yorke even after relaxing certain assumptions in the proof. In addition, we extend the theory to derive the conditions for the existence of chaos in the sense of Devaney. We show that these results can be applied to study the chaotification of linear switching systems.
UR - http://www.scopus.com/inward/record.url?scp=64049119206&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2007.06.109
DO - 10.1016/j.chaos.2007.06.109
M3 - Journal article
SN - 0960-0779
VL - 39
SP - 2225
EP - 2232
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
IS - 5
ER -