Results 1 to 10 of about 170,965 (333)
On the pitchfork bifurcation for the Chafee–Infante equation with additive noise [PDF]
Probability Theory and Related Fields, 2021 We investigate pitchfork bifurcations for a stochastic reaction diffusion equation perturbed by an infinite-dimensional Wiener process. It is well-known that the random attractor is a singleton, independently of the value of the bifurcation parameter ...
A. Blumenthal +2 more
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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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Bifurcation of Dividing Surfaces Constructed from a Pitchfork Bifurcation of Periodic Orbits in a Symmetric Potential Energy Surface with a Post-Transition-State Bifurcation [PDF]
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2021 In this work, we analyze the bifurcation of dividing surfaces that occurs as a result of a pitchfork bifurcation of periodic orbits in a two degrees of freedom Hamiltonian System.
M. Katsanikas, M. Agaoglou, S. Wiggins
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The Pitchfork Bifurcation [PDF]
International Journal of Bifurcation and Chaos, 2016 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.
I. Rajapakse, S. Smale
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Non-smooth pitchfork bifurcations
Discrete & Continuous Dynamical Systems - B, 2004 The author considers the relationship between the blow-out bifurcation and another bifurcation which creates a pair of stable invariant curves and can properly be called a generalized pitchfork bifurcation. The goal of this paper is to show that the two types of bifurcation (generalized) described above are really part of the same generalized ...
Paul Glendinning
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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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Fronts in the Wake of a Parameter Ramp: Slow Passage through Pitchfork and Fold Bifurcations [PDF]
SIAM Journal on Applied Dynamical Systems, 2022 This work studies front formation in the Allen-Cahn equation with a parameter heterogeneity which slowly varies in space. In particular, we consider a heterogeneity which mediates the local stability of the zero state and subsequent pitchfork bifurcation
Ryan N. Goh +3 more
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The effect of noise on pitchfork and Hopf bifurcations [PDF]
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 1997 Summary: We present the results of an experimental and numerical investigation of the effects of noise on pitchfork and Hopf bifurcations. Good quantitative agreement is found between calculations and experiment. In the case of the pitchfork we find that natural imperfections override the effects of the noise. However, novel noise amplification effects
Juel, Anne +2 more
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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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A stochastic pitchfork bifurcation in a reaction-diffusion equation [PDF]
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2001 We study in some detail the structure of the random attractor for the Chafee{Infante reaction{di¬usion equation perturbed by a multiplicative white noise, du = (¢u + u ¡ u3) dt + ¼ u ¯ dWt; x 2 D » Rm: First we prove, for m 65, a lower bound on the dimension of the random attractor, which is of the same order in as the upper ...
Caraballo Garrido, Tomás +2 more
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