Nonlinear Dynamics

, Volume 62, Issue 4, pp 717–727 | Cite as

Multi-stability and basin crisis in synchronized parametrically driven oscillators

  • Olasunkanmi I. Olusola
  • Uchechukwu E. Vincent
  • Abdulahi N. Njah
Original Paper


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.


Synchronization Multi-stability Coupled parametrically excited pendula Chaos Basins crisis 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Olasunkanmi I. Olusola
    • 1
  • Uchechukwu E. Vincent
    • 2
    • 3
  • Abdulahi N. Njah
    • 1
  1. 1.Department of PhysicsUniversity of AgricultureAbeokutaNigeria
  2. 2.Department of PhysicsOlabisi Onabanjo UniversityAgo-IwoyeNigeria
  3. 3.Nonlinear Biomedical Physics, Department of PhysicsLancaster UniversityLancasterUK

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