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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New methods for computing a saddle-node bifurcation point for voltage stability analysis [PDF]
, 1995 This paper proposes methods for calculating saddle-node bifurcation points of power system power flow equations. The first method calculates a saddle-node bifurcation point along a given ray in the parameter space of power flow equations.
Jin Lu, Chih‐Wen Liu, James S. Thorp
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On generation of a limit cycle from a separatrix loop of a sewn saddle-node [PDF]
Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика, 2022 The article considers dynamical systems on the plane, defined by continuous piecewise smooth vector fields. Such systems are used as mathematical models of real processes with switching.
Roitenberg, Vladimir Shleymovich
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Dynamical analysis of an aquatic amensalism model with non-selective harvesting and Allee effect
Mathematical Biosciences and Engineering, 2021 In this paper, in order to explore the inhibition mechanism of algicidal bacteria on algae, we constructed an aquatic amensalism model with non-selective harvesting and Allee effect.
Huanyi Liu +5 more
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Tilting and Squeezing: Phase Space Geometry of Hamiltonian Saddle-Node Bifurcation and its Influence on Chemical Reaction Dynamics [PDF]
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2019 In this article we present the influence of a Hamiltonian saddle-node bifurcation on the high-dimensional phase space structures that mediate reaction dynamics.
V. J. García-Garrido +2 more
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Are physiological oscillations physiological?
The Journal of Physiology, EarlyView., 2023 Abstract figure legend Mechanisms and functions of physiological oscillations. Abstract Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function.
Lingyun (Ivy) Xiong, Alan Garfinkel
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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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