Results 231 to 240 of about 26,001 (267)

Saddle-node bifurcations for hyperbolic sets

Ergodic Theory and Dynamical Systems, 2002
Hyperbolic sets are robust under perturbations: they persist on an open set of the parameter space. In this paper we investigate the boundary of this open set. Generalizing the theory of fixed points we define saddle-node bifurcations for hyperbolic sets K with one-dimensional unstable directions.
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The Saddle-Node Separatrix-Loop Bifurcation

SIAM Journal on Mathematical Analysis, 1987
In the paper vector fields \(x'=f(x)\), \(x\in {\mathbb{R}}^ 2\), having at some point an equilibrium of saddle-node type with a separatrix loop, are studied. Such vector fields fill a codimension two submanifold \(\Sigma\) of an appropriate Banach space. Author gives analytic conditions that determine whether a two-parameter perturbation of \(x'=f(x)\)
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On saddle-node bifurcation and chaos of satellites

Nonlinear Analysis: Theory, Methods & Applications, 1997
The author considers a model of satellite consisting of two masses connected by a rigid rod. The center of mass \(K\) moves on a Keplerian orbit and air drag is taken into account. When \(K\) moves on a circular orbit, the attitude dynamics is governed by an autonomous system of equations while non-zero eccentricity of the orbit of \(K\) introduces ...
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Saddle-Node Bifurcations of Cycles in a Relief Valve

Nonlinear Dynamics, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Discontinuous immittance due to a saddle node bifurcation

Journal of Electroanalytical Chemistry, 1998
The 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, Claude Montella, Jean-Paul Diard, Fabienne Berthier   +3 more
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Automatic Detection of Saddle-Node-Transcritical Interactions

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2019
Dynamical systems with special structure can exhibit transcritical bifurcations of codimension one. In such systems, the interactions of transcritical bifurcations of codimension two can act as organizing centers.
L. Veen, Marvin Hoti
semanticscholar   +1 more source

Control of saddle-node bifurcations in a power system

Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01) (Cat. No.01CH37204), 2002
A 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, J.A. Gallegos, D.I.R. Almeida, C.A. Hernandez   +3 more
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Control of the saddle-node and transcritical bifurcations

IFAC Proceedings Volumes, 2004
Abstract 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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BASIN ORGANIZATION PRIOR TO A TANGLED SADDLE-NODE BIFURCATION

International Journal of Bifurcation and Chaos, 1991
Heteroclinic and homoclinic connections of saddle cycles play an important role in basin organization. In this study, we outline how these events can lead to an indeterminate jump to resonance from a saddle-node bifurcation. Here, due to the fractal structure of the basins in the vicinity of the saddle-node, we cannot predict to which available ...
Mohamed S. Soliman, J. M. T. Thompson
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Critical saddle-node bifurcations and Morse–Smale maps

Physica D: Nonlinear Phenomena, 2004
The authors study the saddle-node bifurcation in diffeomorphisms with a critical homoclinic orbit to a saddle point. More precisely, one considers a typical smooth family \(F_{\gamma}\) of diffeomorphisms that undergoes a saddle-node bifurcation at \(\gamma=0\). For \(\gamma0\).
Todd Young, Brian R. Hunt
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