Results 21 to 30 of about 890 (173)
Transcritical and zero-Hopf bifurcations in the Genesio system [PDF]
Nonlinear Dynamics, 2016 Agraïments: The first author is supported by FAPESP Grant No. 2013/24541-0. Both authors are supported by CAPES Grant 88881.030454/2013-01 Program CSF-PVE. In this paper we study the existence of transcritical and zero--Hopf bifurcations of the third--order ordinary differential equation a b c x - x^2 = 0, called the Genesio equation, which has a ...
Pedro Toniol Cardin, Jaume Llibre
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Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria
The Scientific World Journal, 2014 The bifurcations of heteroclinic loop with one nonhyperbolic equilibrium and one hyperbolic saddle are considered, where the nonhyperbolic equilibrium is supposed to undergo a transcritical bifurcation; moreover, the heteroclinic loop has an orbit flip ...
Fengjie Geng, Junfang Zhao
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Imperfect transcritical and pitchfork bifurcations
Journal of Functional Analysis, 2007 Let \(X\) and \(Y\) be Banach spaces, \(F: \mathbb{R} \times X \to Y\) a nonlinear differentiable map. The authors study the bifurcations of solutions for the equation \[ F(\lambda, u) = 0 \] in a neighborhood of a point \((\lambda_0, u_0)\) under the following assumptions: (F1) \(\dim N\left(F_u\left(\lambda_0,u_0\right)\right) = \text{codim}\,R \left(
Liu, Ping, Shi, Junping, Wang, Yuwen
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Discretizing the transcritical and pitchfork bifurcations – conjugacy results [PDF]
Journal of Difference Equations and Applications, 2015 We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions on the one-step discretization method of order $p\ge 1$, we show that the time-$h$ exact and the step-size-$h$ discretized ...
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Transcritical Bifurcations and Algebraic Aspects of Quadratic Multiparametric Families
WSEAS TRANSACTIONS ON MATHEMATICS, 2021 This article reveals an analysis of the quadratic systems that hold multiparametric families therefore, in the first instance the quadratic systems are identified and classified in order to facilitate their study and then the stability of the critical points in the finite plane, its bifurcations, stable manifold and lastly, the stability of the ...
Contreras, Jorge Rodríguez +3 more
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Bifurcation and Chaotic Behavior of a Discrete-Time SIS Model
Discrete Dynamics in Nature and Society, 2013 The discrete-time epidemic model is investigated, which is obtained using the Euler method. It is verified that there exist some dynamical behaviors in this model, such as transcritical bifurcation, flip bifurcation, Hopf bifurcation, and chaos.
Junhong Li, Ning Cui
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Scientific Reports, 2023 Using a semidiscretization method, we derive in this paper a discrete slow-fast predator-prey system with ratio-dependent functional response. First of all, a detailed study for the local stability of fixed points of the system is obtained by invoking an
Xianyi Li, Jiange Dong
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Mathematics, 2020 We proposed and analyzed a predator–prey model with both the additive Allee effect and the fear effect in the prey. Firstly, we studied the existence and local stability of equilibria.
Liyun Lai, Zhenliang Zhu, Fengde Chen
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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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Metamorphosis of plasma turbulence–shear-flow dynamics through a transcritical bifurcation [PDF]
Physical Review E, 2002 17 pages, revtex text, 9 figures comprised of 16 postscript files. Submitted to Phys.
Ball, Rowena, Dewar, Robert, Sugama, H
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