Bogdanov-Takens singularity of a neural network model with delay
Electronic Journal of Differential Equations, 2016 In this article, we study Bogdanov-Takens (BT) singularity of a tree-neuron model with time delay. By using the frameworks of Campbell-Yuan [2] and Faria-Magalhaes [4,5], the normal form on the center manifold is derived for this singularity and hence
Xiaoqin P. Wu
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Complex dynamics and control analysis of an epidemic model with non-monotone incidence and saturated treatment. [PDF]
Int J Dyn Control, 2023 Saha P, Ghosh U.
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Complete Hopf and Bogdanov-Takens Bifurcation Analysis on Two Epidemic Models [PDF]
, 2022 Infectious diseases are a global problem that harms people’s health and well-being and severely threatens human survival. As an epidemiological model, the SIR model is commonly referred to as forecasting how illnesses will spread, how many people will become sick, and how long an epidemic will last. It is also possible to estimate other epidemiological
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Bifurcation analysis of the predator-prey model with the Allee effect in the predator. [PDF]
J Math Biol, 2021 Sen D, Ghorai S, Banerjee M, Morozov A.
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Bifurcation Analysis of a Generalist Predator-Prey Model with Holling Type II Harvesting
AxiomsIn this paper, we consider a generalist predator–prey model with nonlinear harvesting, which has at most eight non-negative equilibria. We prove that the double positive equilibrium is a cusp of codimension up to 3; therefore, the system exhibits a cusp ...
Mengxin He, Yiqin Wang
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Self-organized criticality in a mesoscopic model of excitatory-inhibitory neuronal populations by short-term and long-term synaptic plasticity. [PDF]
Front Comput Neurosci, 2022 Ehsani M, Jost J.
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An efficient solution procedure for solving higher-codimension Hopf and Bogdanov–Takens bifurcations
Communications in Nonlinear Science and Numerical SimulationIn solving real world systems for higher-codimension bifurcation problems, one often faces the difficulty in computing the normal form or the focus values associated with generalized Hopf bifurcation, and the normal form with unfolding for higher-codimension Bogdanov-Takens bifurcation.
Zeng, Bing, Yu, Pei, Han, Maoan
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Dynamics near manifolds of equilibria of codimension one and bifurcation without parameters
, 2010 We investigate the breakdown of normal hyperbolicity of a manifold of equilibria of a flow. In contrast to classical bifurcation theory we assume the absence of any flow-invariant foliation at the singularity transverse to the manifold of equilibria.
Liebscher, Stefan
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Semi-global analysis of periodic and quasi-periodic k:1 and k:2 resonances [PDF]
The present paper investigates a family of nonlinear oscillators at Hopf bifurcation, driven by a small quasi-periodic forcing. In particular, we are interested in the situation that at bifurcation and for vanishing forcing strength, the driving ...
Wagener, F.O.O.
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