Results 221 to 230 of about 21,597 (261)

Explosions: global bifurcations at heteroclinic tangencies

Ergodic Theory and Dynamical Systems, 2002
We investigate bifurcations in the chain recurrent set for a particular class of one-parameter families of diffeomorphisms in the plane. We give necessary and sufficient conditions for a discontinuous change in the chain recurrent set to occur at a point of heteroclinic tangency.
Alligood, K., Sander, E., Yorke, J.
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Examples of Global Bifurcation

2016
The main goal of this chapter is to give examples of five different types of global bifurcation. While the local bifurcations of the previous chapter were associated with stability changes in an equilibrium, the bifurcations in this chapter are associated with stability changes in a periodic solution. We make no pretense of completeness.
David G. Schaeffer, John W. Cain
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GLOBAL ANALYSIS OF STOCHASTIC BIFURCATION IN DUFFING SYSTEM

International Journal of Bifurcation and Chaos, 2003
Stochastic bifurcation of a Duffing system subject to a combination of a deterministic harmonic excitation and a white noise excitation is studied in detail by the generalized cell mapping method using digraph. It is found that under certain conditions there exist two stable invariant sets in the phase space, associated with the randomly perturbed ...
Wei Xu 0009, Qun He, Tong Fang, Haiwu Rong   +3 more
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Buckling of a critically tapered rod: global bifurcation

Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2003
The present paper, which can be considered as a continuation of the first author's previous papers [\textit{C. A. Stuart}, J. Math. Pures Appl., IX. Sér. 80, No. 3, 281--337 (2001; Zbl 1056.74019) and Proc. R. Soc. Edinb., Sect. A, Math. 132, No. 3, 729--764 (2002; Zbl 1020.34076)] is concerned with studying the buckling of a tapered rod. This physical
Stuart, Charles Alexander, Vuillaume, Grégory   +1 more
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A Global Bifurcation Result for Variational Inequalities

2006
The existence of global bifurcation branch for variational inequalities of a particular type is proved. The proofs is based on a local equivalence of the inequality with a certain equation for which Dancer´s global bifurcation theorem is used.
Kučera, M. (Milan), Eisner, J. (Jan), Recke, L.   +2 more
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GLOBAL BIFURCATIONS AND CHAOTIC DYNAMICS IN SUSPENDED CABLES

International Journal of Bifurcation and Chaos, 2009
The global bifurcations and chaotic dynamics of parametrically and externally excited suspended cables are investigated in this paper. The governing equations are obtained to describe the nonlinear transverse vibrations of suspended cables. The Galerkin procedure is introduced to simplify the governing equations of motion to ordinary differential ...
Hongkui Chen, Zhaohua Zhang, Jilong Wang 0003, Qingyu Xu   +3 more
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GLOBAL AND LOCAL CONTROL OF HOMOCLINIC AND HETEROCLINIC BIFURCATIONS

International Journal of Bifurcation and Chaos, 2005
A comprehensive resonant optimal control method is developed and discussed for suppressing homoclinic and heteroclinic bifurcations of a general one-degree-of-freedom nonlinear oscillator. Based on an adjustable phase shift, the primary resonant optimal control method is presented.
Hongjun Cao, Guanrong Chen
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Global attractors and bifurcations

1996
We present some recent developments in the study of attractors of smooth dynamical systems, specially attractors whose basin has a global character. A key point in our approach is to explore the relations between this study and that of main bifurcation mechanisms.
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A Remark on Real Parameter Global Bifurcation

Acta Mathematica Hungarica, 1998
The paper treats the nonlinear eigenvalue problem \(F(x,\lambda) = L(\lambda)x + R(x,\lambda)=0\), where \(F: X\times {\mathbb{R}} \mapsto X\) with \(X\) a Hilbert space. If \(L(\lambda)\) is a polynomial in \(\lambda\), then it is shown that under some easily verifiable conditions \(\lambda_0 > 0\) is a global bifurcation point.
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Global Bifurcations and Explosions

2018
Nonsmooth systems suffer a curse of dimensionality. Every higher dimension brings the possibility of fundamentally new local and global dynamics, as a simple object classified in low dimensions takes on unknown new complications in higher dimensions. Classifying these conventionally, by forming an accounting of all singularities and their unfoldings ...
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