Results 11 to 20 of about 12,799 (220)
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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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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Bifurcations of global reinjection orbits near a saddle-node Hopf bifurcation [PDF]
Nonlinearity, 2006 The saddle-node Hopf bifurcation (SNH) is a generic codimension-two bifurcation of equilibria of vector fields in dimension at least three. It has been identified as an organizing centre in numerous vector field models arising in applications. We consider here the case that there is a global reinjection mechanism, because the centre manifold of the ...
Bernd Krauskopf, Bart E. Oldeman
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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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Saddle-Node Bifurcation and Homoclinic Persistence in AFMs with Periodic Forcing [PDF]
Mathematical Problems in Engineering, 2019 We study the dynamics of an atomic force microscope (AFM) model, under the Lennard‐Jones force with nonlinear damping and harmonic forcing. We establish the bifurcation diagrams for equilibria in a conservative system. Particularly, we present conditions that guarantee the local existence of saddle‐node bifurcations.
Alexánder Gutiérrez +2 more
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Sensitivity enhancement of nonlinear micromechanical sensors using parametric symmetry breaking [PDF]
Microsystems & NanoengineeringThe working mechanism of resonant sensors is based on tracking the frequency shift in the linear vibration range. Contrary to the conventional paradigm, in this paper, we show that by tracking the dramatic frequency shift of the saddle-node bifurcation ...
Yutao Xu +3 more
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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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Scaling of saddle-node bifurcations: degeneracies and rapid quantitative changes [PDF]
Journal of Physics A: Mathematical and Theoretical, 2008 The scaling of the time delay near a "bottleneck" of a generic saddle-node bifurcation is well-known to be given by an inverse square-root law. We extend the analysis to several non-generic cases for smooth vector fields. We proceed to investigate $C^0$ vector fields.
Christian Kuehn
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Chaos via Shilnikov’s Saddle-Node Bifurcation in a Theory of the Electroencephalogram [PDF]
Physical Review Letters, 2006 We study the bifurcation diagram of a mesoscopic model of the human cortex. This model is known to exhibit robust chaotic behavior in the space of parameters that model exterior forcing. We show that the bifurcation diagram has an unusual degree of organization.
Lennaert van Veen, David T. J. Liley
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