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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 915614, 14 pages
http://dx.doi.org/10.1155/2015/915614
Research Article

Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay

Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, China

Received 22 November 2014; Accepted 20 January 2015

Academic Editor: Garyfalos Papashinopoulos

Copyright © 2015 Wenjie Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Rank one strange attractor in periodically kicked Lorenz system with time-delay is investigated. Our discussion is based on the theory of rank one maps formulated by Wang and Young. First, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when periodically kicked delayed system undergoes a generic Hopf bifurcation. Then we use the theory to the periodically kicked Lorenz system with delay, and derivation of conditions for Hopf bifurcation and rank one chaos along with the results of numerical simulations are presented.