Chaotification of Impulsive Systems by Perturbations

AKHMET M., Fen M. O.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, vol.24, no.6, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 6
  • Publication Date: 2014
  • Doi Number: 10.1142/s0218127414500783
  • Journal Name: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Chaotic impulsive systems, Li-Yorke chaos, chaotic set of piecewise continuous functions, Duffing oscillator, discontinuous chaos control, LI-YORKE CHAOS, LORENZ SYSTEMS, COMPLEX DYNAMICS, SYNCHRONIZATION, NETWORKS, COMMUNICATION, STABILIZATION, STABILITY, FEEDBACK, SPACES
  • TED University Affiliated: No

Abstract

In this paper, we present a new method for chaos generation in nonautonomous impulsive systems. We prove the presence of chaos in the sense of Li-Yorke by implementing chaotic perturbations. An impulsive Duffing oscillator is used to show the effectiveness of our technique, and simulations that support the theoretical results are depicted. Moreover, a procedure to stabilize the unstable periodic solutions is proposed.