Results 221 to 230 of about 21,432 (265)
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Infinite Period Bifurcation and Global Bifurcation Branches
SIAM Journal on Applied Mathematics, 1981Branches of periodic solutions which exhibit the alternatives of the global Hopf bifurcation theorem are calculated for two general systems of differential equations.
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2001
To introduce some local and global bifurcation theory in the plane. To bifurcate limit cycles in the plane. On completion of this chapter, the reader should be able to bifurcate small-amplitude limit cycles from fine foci; bifurcate limit cycles from a center.
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To introduce some local and global bifurcation theory in the plane. To bifurcate limit cycles in the plane. On completion of this chapter, the reader should be able to bifurcate small-amplitude limit cycles from fine foci; bifurcate limit cycles from a center.
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Global Hopf-bifurcation in a neural netlet
Applied Mathematics and Computation, 1998It is investigated the global Hopf bifurcation of periodic solutions to the system of two integro-differential equations describing the dynamics of a neural netlet of activation and inhibition with continuously distributed delays. Naturally in the corresponding differential system [\textit{K. Gopalsamy} and \textit{I. Leung}, Physica D 89, No. 3-4, 395-
K. Gopalsamy +2 more
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Explosions: global bifurcations at heteroclinic tangencies
Ergodic Theory and Dynamical Systems, 2002We 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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GLOBAL ANALYSIS OF STOCHASTIC BIFURCATION IN DUFFING SYSTEM
International Journal of Bifurcation and Chaos, 2003Stochastic 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 +3 more
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Examples of Global Bifurcation
2016The 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 BIFURCATIONS AND CHAOTIC DYNAMICS IN SUSPENDED CABLES
International Journal of Bifurcation and Chaos, 2009The 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 +3 more
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A Global Bifurcation Result for Variational Inequalities
2006The 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) +2 more
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GLOBAL AND LOCAL CONTROL OF HOMOCLINIC AND HETEROCLINIC BIFURCATIONS
International Journal of Bifurcation and Chaos, 2005A 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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A Remark on Real Parameter Global Bifurcation
Acta Mathematica Hungarica, 1998The 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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