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Saddle-Node Bifurcations in Classical and Memristive Circuits [PDF]
International Journal of Bifurcation and Chaos, 2016 This paper addresses a systematic characterization of saddle-node bifurcations in nonlinear electrical and electronic circuits. Our approach is a circuit-theoretic one, meaning that the bifurcation is analyzed in terms of the devices’ characteristics and the graph-theoretic properties of the digraph underlying the circuit.
Ignacio Garcı́a de la Vega +1 more
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Saddle-node bifurcation of viscous profiles.
Physica D, 2012 Traveling wave solutions of viscous conservation laws, that are associated to Lax shocks of the inviscid equation, have generically a transversal viscous profile. In the case of a non-transversal viscous profile we show by using Melnikov theory that a parametrized perturbation of the profile equation leads generically to a saddle-node bifurcation of ...
Achleitner F, Szmolyan P.
europepmc +4 more sources
A double saddle-node bifurcation theorem
Communications on Pure & Applied Analysis, 2013 In this paper, we consider an abstract equation $F(\lambda,u)=0$ with one parameter $\lambda$, where $F\in C^p(\mathbb{R} \times X, Y)$, $p\geq 2$, is a nonlinear differentiable mapping, and $X,Y$ are Banach spaces. We apply Lyapunov-Schmidt procedure and Morse Lemma to obtain a "double" saddle-node bifurcation theorem with a two-dimensional ...
Ping Liu, Junping Shi, Yuwen Wang
semanticscholar +4 more sources
Regularization of the Boundary-Saddle-Node Bifurcation [PDF]
Advances in Mathematical Physics, 2018 In this paper we treat a particular class of planar Filippov systems which consist of two smooth systems that are separated by a discontinuity boundary. In such systems one vector field undergoes a saddle-node bifurcation while the other vector field is ...
Xia Liu
doaj +3 more sources
Scaling properties of saddle-node bifurcations on fractal basin boundaries [PDF]
Physical Review E, 2003 24 pages, 20 ...
Romulus Breban +2 more
openalex +7 more sources
CkSmoothness of Invariant Curves in a Global Saddle-Node Bifurcation
Journal of Differential Equations, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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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