Results 21 to 30 of about 35,466 (285)
Scaling properties of saddle-node bifurcations on fractal basin boundaries [PDF]
Physical Review E, 2003 24 pages, 20 ...
Romulus Breban +2 more
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CkSmoothness of Invariant Curves in a Global Saddle-Node Bifurcation
Journal of Differential Equations, 1996 AbstractThe birth ofCk-smooth invariant curves from a saddle-node bifurcation in a family ofCkdiffeomorphisms on a Banach manifold (possibly infinite dimensional) is constructed in the case that the fixed point is a stable node along hyperbolic directions, and has a smooth noncritical curve of homoclinic orbits.
Todd Young
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Intermittency and Jakobson's theorem near saddle-node bifurcations [PDF]
Discrete & Continuous Dynamical Systems - A, 2007 We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node 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 are supported on the largest possible interval.
Ale Jan Homburg, Todd Young
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Scale-free patterns at a saddle-node bifurcation in a stochastic system [PDF]
Physical Review E, 2008 We demonstrate that scale-free patterns are observed in a spatially extended stochastic system whose deterministic part undergoes a saddle-node bifurcation. Remarkably, the scale-free patterns appear only at a particular time in relaxation processes from a spatially homogeneous initial condition.
Mami Iwata, Shin‐ichi Sasa
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Jacobson's Theorem near saddle-node bifurcations
, 2001 We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node 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.
Ale Jan Homburg, Todd Young
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Scholarpedia, 2006 For the following differential equation, sketch all of the qualitatively different vector fields that occur as r is varied. Show that a saddle-node bifurcation occurs at the critical value r = r c.
Y. Kuznetsov
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An isolated saddle-node bifurcation occurring inside a horseshoe [PDF]
Dynamics and Stability of Systems, 2000 In this paper, we consider a smooth arc of diffeomorphisms which has a saddle-node bifurcation inside a nontrivial invariant set which is a deformation of a horseshoe. We show that this saddle-node bifurcation is isolated, that is, its hyperbolicity is maintained before and after the saddle-node bifurcation.
Yongluo Cao, Shin Kiriki
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Quasi-transversal saddle-node bifurcation on surfaces [PDF]
Ergodic Theory and Dynamical Systems, 1990 AbstractIn this paper we give a complete set of invariants (moduli) for mild and strong semilocal equivalence for certain two parameter families of diffeomorphisms on surfaces. These families exhibit a quasi-transversal saddle-connection between a saddle-node and a hyperbolic periodic point.
Jorge A Beloqui, Maria José Pacífico
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Excitability in a model with a saddle-node homoclinic bifurcation
Discrete & Continuous Dynamical Systems - B, 2004 In order to describe excitable reaction-diffusion systems, we derive a two-dimensional model with a Hopf and a semilocal saddle-node homoclinic bifurcation. This model gives the theoretical framework for the analysis of the saddle-node homoclinic bifurcation as observed in chemical experiments, and for the concepts of excitability and excitability ...
Rui Dilão, András Volford
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Transient periodic behaviour related to a saddle-node bifurcation [PDF]
Journal of Physics A: Mathematical and General, 1987 The authors investigate transient periodic orbits of dissipative invertible maps of R2. Such orbits exist just before, in parameter space, a saddle-node pair is formed. They obtain numerically and analytically simple scaling laws for the duration of the transient, and for the region of initial conditions which evolve into transient periodic orbits.
Ruud van Damme, T. P. Valkering
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