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Multi-stability and basin crisis in synchronized parametrically driven oscillators

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Abstract

This paper studies the synchronization dynamics of two linearly coupled parametrically excited oscillators. The Lyapunov stability theory is employed to obtain some sufficient algebraic criteria for global asymptotic stability of the synchronization of the systems, and an estimated critical coupling, k cr, for which synchronization could be observed is determined. The synchronization transition is found to be associated with the boundary crisis of the chaotic attractor. In the bistable states, where two asymmetric T-periodic attractors co-exist, we show that the coupled oscillators can attain multi-stability via a new dynamical transition—the basin crisis wherein two co-existing attractors are destroyed while new co-existing attractors are created. The stability of the steady states is examined and the possible bifurcation routes identified.

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Author notes

  1. Uchechukwu E. Vincent

    Present address: Nonlinear Biomedical Physics, Department of Physics, Lancaster University, LA1 4YB, Lancaster, UK

Authors and Affiliations

  1. Department of Physics, University of Agriculture, P.M.B. 2240, Abeokuta, Nigeria

    Olasunkanmi I. Olusola & Abdulahi N. Njah

  2. Department of Physics, Olabisi Onabanjo University, P.M.B. 2002, Ago-Iwoye, Nigeria

    Uchechukwu E. Vincent

Authors
  1. Olasunkanmi I. Olusola
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  2. Uchechukwu E. Vincent
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  3. Abdulahi N. Njah
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Correspondence to Olasunkanmi I. Olusola.

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Olusola, O.I., Vincent, U.E. & Njah, A.N. Multi-stability and basin crisis in synchronized parametrically driven oscillators. Nonlinear Dyn 62, 717–727 (2010). https://doi.org/10.1007/s11071-010-9756-9

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  • DOI: https://doi.org/10.1007/s11071-010-9756-9

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