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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
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 +3 more sources
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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Backward bifurcation and saddle-node bifurcation in virus-immune dynamics [PDF]
arXiv, 2021 Recently, Wang and Xu [ Appl. Math. Lett. 78 (2018) 105-111] studied thresholds and bi-stability in virus-immune dynamics. In this paper, we show there also exist backward bifurcation and saddle node bifurcation in this model. Our investigation demonstrates the existence of post-bifurcation phenomenon in the system when the immune strength was selected
Wang, Tengfei, Wang, Shaoli, Xu, Fei
arxiv +3 more sources
Universal Scaling in Saddle-Node Bifurcation Cascades (II) Intermittency Cascade [PDF]
arXiv, 2005 The presence of saddle-node bifurcation cascade in the logistic equation is associated with an intermittency cascade; in a similar way as a saddle-node bifurcation is associated with an intermittency. We merge the concepts of bifurcation cascade and intermittency.
Jesús San-Martín
arxiv +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
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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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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
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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
openalex +4 more sources