Results 21 to 30 of about 26,001 (267)
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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Boundary Driven Waveguide Arrays: Supratransmission and Saddle-Node Bifurcation [PDF]
SIAM Journal on Applied Mathematics, 2008 In this paper, we consider a semi-infinite discrete nonlinear Schrodinger equation driven at one edge by a driving force. The equation models the dynamics of coupled waveguide arrays. When the frequency of the forcing is in the allowed band of the system,
H. Susanto
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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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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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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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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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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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IEEE AccessIn the recent years, significant research interest has been devoted in the modelling and applications of chaotic systems with stable equilibria. In this research study, we propose a new 3-D chaotic system with two stable node-foci equilibria and an ...
Talal Bonny +4 more
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Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: a case study from dynamo theory [PDF]
, 2004 We consider a model of a Hopf bifurcation interacting as a codimension 2 bifurcation with a saddle-node on a limit cycle, motivated by a low-order model for magnetic activity in a stellar dynamo.
Peter Ashwin +2 more
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Time-dependent saddle-node bifurcation: Breaking time and the point of no return in a non-autonomous model of critical transitions. [PDF]
Physica D, 2019 There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle-node bifurcations.
Li JH, Ye FX, Qian H, Huang S.
europepmc +2 more sources