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On the effect of multiplicative noise in a supercritical pitchfork bifurcation
, 2010 The most important characteristic of {\em multiplicative noise} is that its effects of system's dynamics depends on the recent system's state. Consideration of multiplicative noise on self-referential systems including biological and economical systems therefore is of importance. In this note we study an elementary example.
Stefan Reimann
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Pitchfork bifurcations of invariant manifolds
Topology and its Applications, 2007 A pitchfork bifurcation of an $(m-1)$-dimensional invariant submanifold of a dynamical system in $\mathbb{R}^m$ is defined analogous to that in $\mathbb{R}$. Sufficient conditions for such a bifurcation to occur are stated and existence of the bifurcated manifolds is proved under the stated hypotheses.
Jyoti Champanerkar, Denis Blackmore
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Pitchfork Bifurcation In A Coupled Cell System [PDF]
Various biological phenomena, like cell differentiation and pattern formation in multicellular organisms, are explained using the bifurcation theory. Molecular network motifs like positive feedback and mutual repressor exhibit bifurcation and are responsible for the emergence of diverse cell types.
Shikhar Raj, Biplab Bose
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Cluster Oscillation of a Fractional-Order Duffing System with Slow Variable Parameter Excitation
Fractal and Fractional, 2022 The complicated dynamic behavior of a fractional-order Duffing system with slow variable parameter excitation is investigated. The stability and bifurcation behavior of the fast subsystem are analyzed by using the dynamic theory of fractional-order ...
Xianghong Li, Yanli Wang, Yongjun Shen
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Stable and non-symmetric pitchfork bifurcations [PDF]
Science China Mathematics, 2020 In this paper, we present a criterion for pitchfork bifurcation of smooth vector fields based on a topological argument. Our result expands Rajapakse and Smale's result \cite{RS2} significantly. Based on our criterion, we present a class of families of non-symmetric vector fields undergoing a pitchfork bifurcation.
Michael Shub +2 more
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The Pitchfork Bifurcation [PDF]
International Journal of Bifurcation and Chaos, 2017 We present the development of a new theory of the pitchfork bifurcation, which removes the perspective of the third derivative and a requirement of symmetry.
Indika Rajapakse, Steve Smale
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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 ...
Lajos Lóczi
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The effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems [PDF]
Journal of Physics A: Mathematical and Theoretical, 2007 LaTex, 25 pp., 14 Figures (26 *.eps files); final version 3, to be published in Journal of Physics ...
Marta Gutiérrez +3 more
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Exploring the mechanisms of differentiation, dedifferentiation, reprogramming and transdifferentiation. [PDF]
PLoS ONE, 2014 We explored the underlying mechanisms of differentiation, dedifferentiation, reprogramming and transdifferentiation (cell type switchings) from landscape and flux perspectives.
Li Xu, Kun Zhang, Jin Wang
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