NDLI: Multi-stability and basin crisis in synchronized parametrically driven oscillators

Content Provider	Springer Nature Link
Author	Olusola, Olasunkanmi I. Vincent, Uchechukwu E. Njah, Abdulahi N.
Copyright Year	2010
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.
Starting Page	717
Ending Page	727
Page Count	11
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	62
Issue Number	4
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-07-11
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Synchronization Multi-stability Coupled parametrically excited pendula Chaos Basins crisis Automotive Engineering Mechanical Engineering Mechanics Vibration, Dynamical Systems, Control
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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