Transcritical bifurcation and Neimark-Sacker bifurcation of a discrete predator-prey model with herd behaviour and square root functional response [PDF]
Mathematical and Computer Modelling of Dynamical SystemsIn this paper, a discrete predator-prey model incorporating herd behaviour and square root response function is deduced from its continuous version by the semi-discretization method.
Danyang Li, Xianyi Li
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Mathematical remarks on transcritical bifurcation in Hamiltonian systems [PDF]
, 2007 This article is meant as a mathematical appendix or comment on [BT]. We first consider the notion of transcritical bifurcations of fixed points of general area-preserving maps, and then adress some questions related to [BT] on bifurcation in Poincar maps of 2-dimensional Hamiltonian systems. [BT] M. Brack and K.
Klaus Jaenich
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The saddle-node-transcritical bifurcation in a population model with constant rate harvesting [PDF]
Discrete & Continuous Dynamical Systems - B, 2010 We study the interaction of saddle-node and transcritical bifurcations in a Lotka-Volterra model with a constant term representing harvesting or migration. Because some of the equilibria of the model lie on an invariant coordinate axis, both the saddle-node and the transcritical bifurcations are of codimension one.
Kie Van Ivanky Saputra +2 more
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A transcritical bifurcation in an immune response model
Journal of Difference Equations and Applications, 2011 The consequences of regulatory T cell (Treg) inhibition of interleukine 2 secretion are examined by mathematical modelling. We find a transcritical bifurcation that might explain two alternative scenarios: in one case the appearance of autoimmune responses and in another the suppression of the immune response.
Nigel J. Burroughs +3 more
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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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Transcritical bifurcation and flip bifurcation of a new discrete ratio-dependent predator-prey system [PDF]
Qualitative Theory of Dynamical Systems, 2022 Abstract After a discrete two-species predator-prey system with ratio-dependent functional response is topologically and equivalently reduced, some new dynamical properties for the new discrete system are formulated. The one is for the existence and local stability for all equilibria of this new system.
Xianyi Li, Yuqing Liu
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Transcritical bifurcations in nonintegrable Hamiltonian systems [PDF]
Physical Review E, 2008 LaTeX, 38 pages, 13 figures; substantially revised version v4; to be published in Phys.
M. Brack, К. Tanaka
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Transcritical bifurcation yielding global stability for network processes
Nonlinear Analysis, 2020 In this paper, the dynamical system \[ \dot x(t)=f(x(t)) \tag{1} \] is considered in the unit cube \(Q=\{x\in \mathbb{R}^n: 0\le x_i\le 1, i=1,\dots,n\}\) where \(f:\mathbb{R}^n\to\mathbb{R}^n\) is a differentiable function. If \(x=0\) is a solution of system (1), the authors specify sufficient conditions of its global asymptotic stability.
Ágnes Bodó, Peter Šimon
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Bifurcation and hybrid control of a discrete eco-epidemiological model with Holling type-III. [PDF]
PLoS ONEIn this paper, a three dimensional discrete eco-epidemiological model with Holling type-III functional response is proposed. Boundedness of the solutions of the system is analyzed.
Lizhi Fei, Hengmin Lv, Heping Wang
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Dynamic analysis and control of a rice-pest system under transcritical bifurcations [PDF]
PeerJ, 2023 A decision model is developed by adopting two control techniques, combining cultural methods and pesticides in a hybrid approach. To control the adverse effects in the long term and to be able to evaluate the extensive use of pesticides on the environment and nearby ecosystems, the novel decision model assumes the use of pesticides only in an emergency
Sajib Mandal +3 more
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