Results 11 to 20 of about 7,167 (323)
Semiclassical trace formulas for pitchfork bifurcation sequences [PDF]
Physical Review E, 2004 In non-integrable Hamiltonian systems with mixed phase space and discrete symmetries, sequences of pitchfork bifurcations of periodic orbits pave the way from integrability to chaos.
J. Kaidel, M. Brack
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Pathwise description of dynamic pitchfork bifurcations with additive noise [PDF]
Probability Theory and Related Fields, 2002 The slow drift (with speed $\eps$) of a parameter through a pitchfork bifurcation point, known as the dynamic pitchfork bifurcation, is characterized by a significant delay of the transition from the unstable to the stable state.
Nils Berglund, Barbara Gentz
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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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Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay
Nonlinear Analysis: Modelling and Control, 2017 In this paper, the Hopf-pitchfork bifurcation of coupled van der Pol with delay is studied. The interaction coefficient and time delay are taken as two bifurcation parameters.
Chunrui 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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Non-smooth pitchfork bifurcations
Discrete & Continuous Dynamical Systems - B, 2004 The bifurcations of strange nonchaotic attractors in quasi-periodically forced systems are poorly understood. A simple two-parameter example is introduced which unifies previous observations of non-smooth pitchfork bifurcations and blowout bifurcations of strange nonchaotic attractors.
Paul Glendinning
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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 We present the results of an experimental and numerical investigation into 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.
Anne Juel, Alan G. Darbyshire, T. Mullin
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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 bound we derived in an ...
Tomás Caraballo +2 more
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On the pitchfork bifurcation for the Chafee-Infante equation with additive noise
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; this phenomenon is often referred to as the "destruction" of the bifurcation by the noise.
Alex Blumenthal +2 more
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