Nonlinear dynamics: Simplicity and universality in the transition to chaos

Alan Wolf

doi:10.1038/305182a0

Nonlinear dynamics: Simplicity and universality in the transition to chaos

Nature ◽

10.1038/305182a0 ◽

1983 ◽

Vol 305 (5931) ◽

pp. 182-183 ◽

Cited By ~ 9

Author(s):

Alan Wolf

Keyword(s):

Nonlinear Dynamics ◽

Transition To Chaos

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Observation of nonlinear dynamics and transition to chaos in Photonic Integrated Circuits

2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference ◽

10.1109/cleoe-iqec.2007.4387004 ◽

2007 ◽

Author(s):

Mirvais Yousefi ◽

Stefano Beri ◽

Y. Barbarin ◽

E.A.J.M. Bente ◽

M.K. Smit ◽

...

Keyword(s):

Nonlinear Dynamics ◽

Integrated Circuits ◽

Photonic Integrated Circuits ◽

Transition To Chaos

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Nonlinear Dynamics of Low Reynolds Number Round Jets: Periodic Attractors and Transition to Chaos

Fluid Mechanics and Its Applications - Advances in Turbulence VII ◽

10.1007/978-94-011-5118-4_25 ◽

1998 ◽

pp. 105-108

Author(s):

Ionut Danaila ◽

Jan Dušek ◽

Fabien Anselmet

Keyword(s):

Nonlinear Dynamics ◽

Reynolds Number ◽

Low Reynolds Number ◽

Round Jets ◽

Transition To Chaos ◽

Periodic Attractors ◽

Low Reynolds

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Intermittent transition to chaos in vibroimpact system

Applied Mathematics and Nonlinear Sciences ◽

10.2478/amns.2018.2.00037 ◽

2018 ◽

Vol 3 (2) ◽

pp. 475-486 ◽

Cited By ~ 8

Author(s):

V.A. Bazhenov ◽

O.S. Pogorelova ◽

T.G. Postnikova

Keyword(s):

Nonlinear Dynamics ◽

Wavelet Transform ◽

Dynamical Systems ◽

Mathematical Tool ◽

Continuous Wavelet ◽

Strongly Nonlinear ◽

Transition To Chaos ◽

Great Confidence ◽

Route To Chaos ◽

Vibroimpact System

AbstractChaotic behaviour of dynamical systems, their routes to chaos, and the intermittency in particular are interesting and investigated subjects in nonlinear dynamics. The studying of these phenomena in non-smooth dynamical systems is of the special scientists’ interest. In this paper we study the type-III intermittency route to chaos in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We apply relatively new mathematical tool – continuous wavelet transform CWT – for investigation this phenomenon. We show that CWT applying allows to detect and determine the chaotic motion and the intermittency with great confidence and reliability, gives the possibility to demonstrate intermittency route to chaos, to distinguish and analyze the laminar and turbulent phases.

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