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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Springer Netherlands

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DOI

10.1016/0022-3697(61)90121-4

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1573-269X

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Metamorphoses of basin boundaries with complex top

Authors: Yongxiang Zhang Huaguang Zhang
Publish Date: 2014/11/28
Volume: 79, Issue: 4, Pages: 2309-2323
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Abstract

In a recent paper we examined a driven archetypal oscillator which is derived from an arch bridge model with a sinusoidally varying central load We showed that this oscillator can possess complex basins of constrained motions in the space of the initial conditions We here investigate the mechanisms for the metamorphoses of basin boundary with topological complexity as the control parameter the magnitude of the excitation varies The Wada basin boundary metamorphoses include the creation or disappearance of some new or old basin sets by a series of saddlenode or inverse saddlenode bifurcations in the Poincaré map The changes can also be induced by the collision between the attractors and the stable or unstable manifold of the regular saddles The mechanism for Wada basin boundary metamorphoses is also investigated by the homoclinic tangency and rotary homoclinic tangency The results perhaps can explain a series of jump phenomena in the mechanical oscillator and give a good guide to safe parameter design according to safe basinThe authors are deeply indebted to all anonymous reviewers for their careful reading of the manuscript as well as for their fruitful comments and advice which led to an improvement of this paper We would like to thank you very much for helping us to correct some minor points in the manuscript This work was supported by the National Natural Science Foundation of China Nos 61034005 61433004 and the National High Technology Research and Development Program of China 2012AA040104 and IAPI Fundamental Research Funds 2013ZCX14 This work was supported also by the development project of key laboratory of Liaoning province

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