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7,952
Constraint at a saddle node bifurcation
, 1993
"... Many power engineering systems have dynamic state variables which can encounter constraints or limits affecting system stability. Voltage collapse is an instability associated with the occurrence of a saddle node bifurcation in the equations which model the electric power system. We investigate the ..."
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Cited by 1 (1 self)
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Many power engineering systems have dynamic state variables which can encounter constraints or limits affecting system stability. Voltage collapse is an instability associated with the occurrence of a saddle node bifurcation in the equations which model the electric power system. We investigate
A double saddlenode bifurcation theorem ∗
"... We consider an abstract equation F(λ, u) = 0 with one parameter λ, where F ∈ C p (R × X, Y), p ≥ 2 is a nonlinear differentiable mapping, and X, Y are Banach spaces. We apply LyapunovSchmidt procedure and Morse Lemma to obtain a “double ” saddlenode bifurcation theorem near a degenerate point wit ..."
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We consider an abstract equation F(λ, u) = 0 with one parameter λ, where F ∈ C p (R × X, Y), p ≥ 2 is a nonlinear differentiable mapping, and X, Y are Banach spaces. We apply LyapunovSchmidt procedure and Morse Lemma to obtain a “double ” saddlenode bifurcation theorem near a degenerate point
Homoclinic SaddleNode Bifurcations in Singularly Perturbed Systems
 J. DYN. DIFF. EQ
, 1997
"... In this paper we study the creation of homoclinic orbits by saddlenode bifurcations. Inspired on similar phenomena appearing in the analysis of socalled `localized structures' in modulation or amplitude equations, we consider a family of nearly integrable, singularly perturbed three dimension ..."
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Cited by 3 (2 self)
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In this paper we study the creation of homoclinic orbits by saddlenode bifurcations. Inspired on similar phenomena appearing in the analysis of socalled `localized structures' in modulation or amplitude equations, we consider a family of nearly integrable, singularly perturbed three
Dynamics of Attention as Near SaddleNode Bifurcation Behavior
 Advances in Neural Information Processing Systems, Volume 8, Neural Information Processing Systems 1995
, 1996
"... In consideration of attention as a means for goaldirected behavior in nonstationary environments, we argue that the dynamics of attention should satisfy two opposing demands: longterm maintenance and quick transition. These two characteristics are contradictory within the linear domain. We propos ..."
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Cited by 4 (1 self)
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propose the near saddlenode bifurcation behavior of a sigmoidal unit with selfconnection as a candidate of dynamical mechanism that satisfies both of these demands. We further show in simulations of the `bugeatfood' tasks that the near saddlenode bifurcation behavior of recurrent networks can
Conditions for saddlenode bifurcations in ac/dc power systems
 J. OF ELECTRIC POWER & ENERGY SYSTEMS
, 1995
"... Saddlenode bifurcations are dynamic instabilities of differential equation models that have been associated with voltage collapse problems in power systems. This paper presents the conditions needed for detecting these types of bifurcations using power flow equations for a dynamic model of ac/dc sy ..."
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Cited by 18 (2 self)
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Saddlenode bifurcations are dynamic instabilities of differential equation models that have been associated with voltage collapse problems in power systems. This paper presents the conditions needed for detecting these types of bifurcations using power flow equations for a dynamic model of ac
Intermittency and Jakobson's theorem near saddlenode bifurcations
, 2003
"... We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddlenode bifurcation. We show that there is a parameter set of positive but not full Lebesgue density at the bifurcation, for which the maps exhibit absolutely continuous invariant measures which ..."
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Cited by 1 (1 self)
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We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddlenode bifurcation. We show that there is a parameter set of positive but not full Lebesgue density at the bifurcation, for which the maps exhibit absolutely continuous invariant measures which
Nonautonomous saddlenode bifurcations: random and deterministic forcing
 J. Differ. Equations
"... ar ..."
Jakobson's Theorem near saddlenode bifurcations
, 2001
"... We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddlenode bifurcation. It was previously shown that for a parameter set of positive Lebesgue density at the bifurcation, the maps possess attracting periodic orbits of high period. We show that the ..."
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We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddlenode bifurcation. It was previously shown that for a parameter set of positive Lebesgue density at the bifurcation, the maps possess attracting periodic orbits of high period. We show
REAL SADDLENODE BIFURCATION FROM A COMPLEX VIEWPOINT
"... Abstract. During a saddlenode bifurcation for real analytic interval maps, a pair of fixed points, attracting and repelling, collide and disappear. From the complex point of view, they do not disappear, but just become complex conjugate. The question is whether those new complex fixed points are at ..."
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Abstract. During a saddlenode bifurcation for real analytic interval maps, a pair of fixed points, attracting and repelling, collide and disappear. From the complex point of view, they do not disappear, but just become complex conjugate. The question is whether those new complex fixed points
Highly Excited Motion in Molecules: SaddleNode Bifurcations and Their Fingerprints in Vibrational Spectra
, 2002
"... The vibrational motion of highly excited molecules is discussed in terms of exact quantum and classical mechanics calculations, employing global potential energy surfaces, as well as in terms of a spectroscopic Hamiltonian and its semiclassical limit. The main focus is saddlenode bifurcations and t ..."
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Cited by 4 (2 self)
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The vibrational motion of highly excited molecules is discussed in terms of exact quantum and classical mechanics calculations, employing global potential energy surfaces, as well as in terms of a spectroscopic Hamiltonian and its semiclassical limit. The main focus is saddlenode bifurcations
Results 1  10
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7,952