Results 1 to 10 of about 178,428 (365)
Pathwise description of dynamic pitchfork bifurcations with additive noise [PDF]
Probability Theory and Related Fields, 2000 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.
Berglund, Nils, Gentz, Barbara
core +13 more sources
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
arxiv +6 more sources
Uniform approximations for pitchfork bifurcation sequences [PDF]
Physical Review E, 2003 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.
A. Erdélyi +13 more
core +11 more sources
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 a pitchfork bifurcation.
Geng, Fengjie, Li, Song
openaire +4 more sources
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
+7 more sources
Symmetries in the Lorenz-96 model [PDF]
International Journal of Bifurcations and Chaos, Vol. 29, No. 1
(2019) 1950008, 2019 The Lorenz-96 model is widely used as a test model for various applications, such as data assimilation methods. This symmetric model has the forcing $F\in\mathbb{R}$ and the dimension $n\in\mathbb{N}$ as parameters and is $\mathbb{Z}_n$ equivariant.
Sterk, Alef E., van Kekem, Dirk L.
core +3 more sources
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.
Juel, Anne +2 more
openaire +4 more sources
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
openaire +5 more sources
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
openaire +3 more sources
Imperfect transcritical and pitchfork bifurcations
Journal of Functional Analysis, 2007 AbstractImperfect bifurcation phenomena are formulated in framework of analytical bifurcation theory on Banach spaces. In particular the perturbations of transcritical and pitchfork bifurcations at a simple eigenvalue are examined, and two-parameter unfoldings of singularities are rigorously established.
Yuwen Wang +4 more
openaire +2 more sources