NDLI: Properties of Chaotic and Regular Boundary Crisis in Dissipative Driven Nonlinear Oscillators

Content Provider	Springer Nature Link
Author	Szemplińska Stupnicka, W. Zubrzycki, A. Tyrkiel, E.
Copyright Year	1999
Abstract	The phenomenon of the chaotic boundary crisis and the related concept of the ‘chaotic destroyer saddle’ has become recently a new problem in the studies of the destruction of chaotic attractors in nonlinear oscillators. As it is known, in the case of regular boundary crisis, the homoclinic bifurcation of the destroyer saddle defines the parameters of the annihilation of the chaotic attractor. In contrast, at the chaotic boundary crisis, the outset of the destroyer saddle which branches away from the chaotic attractor is tangled prior to the crisis. In our paper, the main point of interest is the problem of a relation, if any, between the homoclinic tangling of the destroyer saddle and the other properties of the system which may accompany the chaotic as well as the regular boundary crisis. In particular, the question if the phenomena of fractal basin boundary, indeterminate outcome, and a period of the destroyer saddle, are directly implied by the structure of the destroyer saddle invariant manifolds, is examined for some examples of the boundary crisis that occur in the mathematical models of the twin-well and the single-well potential nonlinear oscillators.
Starting Page	19
Ending Page	36
Page Count	18
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	19
Issue Number	1
e-ISSN	1573269X
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1999-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mechanics Vibration, Dynamical Systems, Control Mechanical Engineering Automotive and Aerospace Engineering, Traffic
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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