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Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation [PDF]
Abstract and Applied Analysis, 2014 The bifurcation of a nongeneric homoclinic orbit (i.e., the orbit comes from the equilibrium along the unstable manifold instead of the center manifold) connecting a nonhyperbolic equilibrium is investigated, and the nonhyperbolic equilibrium undergoes ...
Fengjie Geng, Song Li
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Hopf-Pitchfork Bifurcation in a Phytoplankton-Zooplankton Model with Delays [PDF]
Abstract and Applied Analysis, 2013 The purpose of this paper is to study the dynamics of a phytoplankton-zooplankton model with toxin delay. By studying the distribution of the eigenvalues of the associated characteristic equation, the pitchfork bifurcation curve of the system is obtained.
Jia-Fang Zhang, Dan Zhang
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On the direction of pitchfork bifurcation
Electronic Journal of Differential Equations, 2007 We present an algorithm for computing the direction of pitchfork bifurcation for two-point boundary value problems. The formula is rather involved, but its computational evaluation is quite feasible. As an application, we obtain a multiplicity result.
Xiaojie Hou, Philip Korman, Yi Li
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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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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.
Rajapakse, Indika, Smale, Steve
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Semiclassical trace formulas for pitchfork bifurcation sequences [PDF]
Physical Review E, 2004 In nonintegrable Hamiltonian systems with mixed phase space and discrete symmetries, sequences of pitchfork bifurcations of periodic orbits pave the way from integrability to chaos. In extending the semiclassical trace formula for the spectral density, we develop a uniform approximation for the combined contribution of pitchfork bifurcation pairs.
J, Kaidel, M, Brack
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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.
Pujals, Enrique +2 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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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.
Champanerkar, Jyoti, Blackmore, Denis
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Slow Passage Through a Pitchfork Bifurcation [PDF]
SIAM Journal on Applied Mathematics, 1996 Summary: This paper deals with a class of second-order differential equations with a slowly varying bifurcation parameter. The parameter slowly varies through a critical value corresponding to a transition from a stable equilibrium to one of the two stable branches of an intersecting parabolic curve.
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