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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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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The Hopf-saddle-node bifurcation for fixed points of 3D-diffeomorphisms: the Arnol'd resonance web
, 2008 A model map Q for the Hopf-saddle-node (HSN) bifurcation of fixed points of diffeomorphisms is studied. The model is constructed to describe the dynamics inside an attracting invariant two-torus which occurs due to the presence of quasi-periodic Hopf ...
Henk Broer, Carles Simö, Renato Vitolo
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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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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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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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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
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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Rate-Induced Tipping and Saddle-Node Bifurcation for Quadratic Differential Equations with Nonautonomous Asymptotic Dynamics [PDF]
SIAM Journal on Applied Dynamical Systems, 2021 An in-depth analysis of nonautonomous bifurcations of saddle-node type for scalar differential equations $x'=-x^2+q(t)\,x+p(t)$, where $q\colon\mathbb{R}\to\mathbb{R}$ and $p\colon\mathbb{R}\to\mathbb{R}$ are bounded and uniformly continuous, is ...
Iacopo P. Longo +3 more
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Numerical Study of One Prey-Two Predator Model Considering Food Addition and Anti-Predator Defense [PDF]
E3S Web of Conferences, 2021 This article examines the interaction between prey populations, juvenile predators, and adult predators. A mathematical model that considers adding food and anti-predators was developed.
Savitri Dian
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