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Adaptive reduced-order function projective synchronization and circuit design o f hyperchaotic DLE with no equilibria

ZHOUCHAO WEI1,* , YANXIA TANG2, HUAI CHEN3, IHSAN PEHLİVAN4

Affiliation

  1. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China
  2. Department of Mathematics, College of Science, Hebei North University, Zhangjiakou 075000, China
  3. Faculty of Earth Sciences, China University of Geosciences, Wuhan, 430074, Chin a
  4. Department of Electrical and Electronics Engineering, Sakarya University,TR 54187,Esentepe Campus, Sakarya, T urkey

Abstract

By introducing a feedback control to a classic DLE system (diffusionless Lorenz equationsequations), an extremely complex hyperchaotic attractor with no equilibria is derived. Based on adaptive control and Lyapunov stability theory, we design a reduced-order projective synchronization scheme for synchronizing the hyperchaotic DLE coexist with no equilibria and the 3 D chaotic Wang-Chen system coexist with one stable equilibri umum, which both do not meet the Sil’nikov criteria. Finally, numerical simulations are given to illustrate the effectiveness of the proposed synchronization scheme, and then its circuit implementation is included as real applications..

Keywords

Hyperchaotic attractors, Reduced-order, Projective synchronization, Lyapunov exponent,Lyapunov stability theorem, Circuit implementation.

Citation

ZHOUCHAO WEI, YANXIA TANG, HUAI CHEN, IHSAN PEHLİVAN, Adaptive reduced-order function projective synchronization and circuit design o f hyperchaotic DLE with no equilibria, Optoelectronics and Advanced Materials - Rapid Communications, 7, 11-12, November-December 2013, pp.984-990 (2013).

Submitted at: June 6, 2013

Accepted at: Nov. 7, 2013