Results 11 to 20 of about 5,207 (226)
Hopf Bifurcations on Cubic Lattices [PDF]
Nonlinearity, 2003 The author continues his previous work in this article. The standard results on equivariant Hopf bifurcation are applied. Explicit computations concerning stability are performed.
Callahan, T. K.
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Global Hopf bifurcation in the ZIP regulatory system [PDF]
, 2015 Regulation of zinc uptake in roots of Arabidopsis thaliana has recently been modeled by a system of ordinary differential equations based on the uptake of zinc, expression of a transporter protein and the interaction between an activator and inhibitor ...
Ptashnyk, Mariya +4 more
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Unfoldings of Singular Hopf Bifurcation [PDF]
SIAM Journal on Applied Dynamical Systems, 2012 Singular Hopf bifurcation occurs in generic families of vector-fields with two slow variables and one fast variable. Normal forms for this bifurcation depend upon several parameters, and the dynamics displayed by the normal forms is intricate. This paper analyzes a normal form for this bifurcation.
John Guckenheimer, Philipp Meerkamp
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Hopf bifurcation in a gene regulatory network model : molecular movement causes oscillations [PDF]
, 2014 M.A.J.C. and M.S. gratefully acknowledge the support of the ERC Advanced Investigator Grant 227619, “M5CGS — From Mutations to Metastases: Multiscale Mathematical Modelling of Cancer Growth and Spread”. M.S.
Ptashnyk, Mariya +10 more
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Bifurcations and Turing patterns in a diffusive Gierer–Meinhardt model
Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, the Hopf bifurcations and Turing bifurcations of the Gierer–Meinhardt activator-inhibitor model are studied. The very interesting and complex spatially periodic solutions and patterns induced by bifurcations are analyzed from both ...
Yong Wang, Mengping Guo, Weihua Jiang
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Rigorous verification of Hopf bifurcations via desingularization and continuation [PDF]
, 2021 In this paper we present a general approach to rigorously validate Hopf bifurcations as well as saddlenode bifurcations of periodic orbits in systems of ODEs.
Queirolo, Elena +3 more
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Dynamics of a plant-herbivore model with a chemically-mediated numerical response
Mathematics in Applied Sciences and Engineering, 2021 A system of two ordinary differential equations is proposed to model chemically-mediated interactions between plants and herbivores by incorporating a toxin-modified numerical response.
Lin Wang, James Watmough, Fang Yu
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Dynamics of a Discretization Physiological Control System
Discrete Dynamics in Nature and Society, 2007 We study the dynamics of solutions of discrete physiological control system obtained by Midpoint rule. It is shown that a sequence of Hopf bifurcations occurs at the positive equilibrium as the delay increases and we analyze the stability of the solution
Xiaohua Ding, Huan Su
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Hopf Bifurcation Analysis of the Halvorsen System
Zanco Journal of Pure and Applied SciencesThis paper investigates local bifurcations in the Halvorsen system, focusing specifically on transcritical and Hopf bifurcations. The behavior of equilibrium points during bifurcations is studied using Sotomayor's theorem for transcritical bifurcation ...
Kardo Baiz Othman, Adnan Ali Jalal
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Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation
Abstract and Applied Analysis, 2013 The dynamics of a 2-dimensional neural network model in neutral form are investigated. We prove that a sequence of Hopf bifurcations occurs at the origin as the delay increases.
Ming Liu, Xiaofeng Xu
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