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A NONAUTONOMOUS SADDLE-NODE BIFURCATION PATTERN
Stochastics and Dynamics, 2004In this paper we study certain differential equations depending on a small parameter ε which exhibit a bifurcation of saddle-node type as ε passes through zero. We use a classical averaging technique together with methods and results from the modern theory of nonautonomous differential equations.
FABBRI, ROBERTA +2 more
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Saddle-node bifurcations in the spectrum of HOCl
The Journal of Chemical Physics, 2000A detailed analysis of the bound-state spectrum of HOCl (hypoclorous acid) in the ground electronic state is presented. Exact quantum mechanical calculations (filter diagonalization) are performed employing an ab initio potential energy surface, which has been constructed using the multireference configuration-interaction method and a quintuple-zeta ...
J. Hauschildt +7 more
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Quantum manifestations of saddle-node bifurcations
Chemical Physics Letters, 1995Abstract We show that the periodic orbits originating from a saddle-node bifurcation have a profound influence on the topology of the vibrational wavefunctions of the LiNC/LiCN molecular system described by a realistic and complex potential energy surface. The underlying classical structures (manifolds) are examined in detail.
A. A. Zembekov +2 more
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Saddle-Node Bifurcations on Fractal Basin Boundaries
Physical Review Letters, 1995We demonstrate and analyze a bifurcation producing a type of fractal basin boundary which has the strange property that any point that is on the boundary of that basin is also simultaneously on the boundary of at least two other basins. We give rigorous general criteria guaranteeing this phenomenon, present illustrative numerical examples, and discuss ...
Helena E. Nusse +2 more
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Saddle node bifurcation in a PLL
Proceedings of Southeastcon '93, 2002New results are given on the phenomenon of false lock in second-order, Type I PLLs (phase-locked loops) with a constant frequency reference of /spl omega//sub i/ and a VCO (voltage-controlled oscillator) quiescent frequency of /spl omega//sub o/. Of interest here is the stable false lock state whose frequency error approaches /spl omega//sub i/-/spl ...
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Discontinuous immittance due to a saddle node bifurcation
Journal of Electroanalytical Chemistry, 1998The Frumkin isotherm for the electrosorption reaction is S-shaped for the interaction parameter values lower than a critical level, leading to a hysteresis loop during steady-state studies. It is shown that isotherm branch switching phenomena can occur during the study of the electrosorption reaction by electrochemical impedance spectroscopy.
B. Le Gorrec +3 more
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The Saddle-Node Separatrix-Loop Bifurcation
SIAM Journal on Mathematical Analysis, 1987We study vector fieldx $\dot x = f(x)$, $x \in \mathbb{R}^2 $, having at some point an equilibrium of saddle-node type with a separatrix loop. Such vector fields fill a codimension two submanifold $\sum $, of an appropriate Banach space. We give analytic conditions that determine whether a two-parameter perturbation of $\dot x = f(x)$ is transverse to $
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Control of saddle-node bifurcations in a power system
Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01) (Cat. No.01CH37204), 2002A bifurcation analysis and controller for a basic power system are presented. The controller, whose objective is to eliminate the saddle-node bifurcation presented in the system, is based on the internal-model control structure for nonlinear systems.
J.V. Mariscal +3 more
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Control of the saddle-node and transcritical bifurcations
IFAC Proceedings Volumes, 2004Abstract In this paper, the control of the saddle-node and transcritical bifurcations in nonlinear systems is treated. A new approach is presented to find sufficient conditions in terms of the original vector fields. The analysis of the system dynamics is reduced to dimension one through the center manifold theorem.
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Critical saddle-node horseshoes: bifurcations and entropy
Nonlinearity, 2003In this paper we study one-parameter families (f?)?[?1,1] of two-dimensional diffeomorphisms unfolding critical saddle-node horseshoes (say at ? = 0) such that f? is hyperbolic for negative ?. We describe the dynamics at some isolated secondary bifurcations that appear in the sequel of the unfolding of the initial saddle-node bifurcation.
Isabel Rios, Lorenzo J. Díaz
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