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https://www.ias.ac.in/article/fulltext/pram/073/06/1011-1022

Chaos; synchronization; boundary crisis; parametrically excited pendula; Lyapunov theory; linear matrix inequality.

In this paper, we study the synchronization behaviour of two linearly coupled parametrically excited chaotic pendula. The stability of the synchronized state is examined using Lyapunov stability theory and linear matrix inequality (LMI); and some sufficient criteria for global asymptotic synchronization are derived from which an estimated critical coupling is determined. Numerical solutions are presented to verify the theoretical analysis. We also examined the transition to stable synchronous state and show that this corresponds to a boundary crisis of the chaotic attractor.

O I Olusola¹ U E Vincent^{2 3 4} A N Njah¹

1. Department of Physics, University of Agriculture, P.M.B. 2240, Abeokuta, Nigeria
2. Department of Nonlinear Dynamics and Statistical Physics, Institute of Theoretical Physics, Technical University of Clausthal, Arnold-Sommer Str. 6, 38678 Clausthal-Zellerfeld, Germany
3. Department of Physics, Nonlinear Biomedical Physics Division, Lancaster University, LA1 4YB Lancaster, UK
4. Permanent address: Department of Physics, Olabisi Onabanjo University, P.M.B. 2002, Ago-Iwoye, Nigeria

Published

December 2009

Manuscript received

24 March 2009

Manuscript revised

8 July 2009

Accepted

30 July 2009