Results 11 to 20 of about 178,428 (365)
On the pitchfork bifurcation for the Chafee–Infante equation with additive noise [PDF]
Probability Theory and Related Fields, 2023 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
semanticscholar +5 more sources
A Stochastic Pitchfork Bifurcation in Most Probable Phase Portraits [PDF]
International Journal of Bifurcation and Chaos, 2018 We study stochastic bifurcation for a system under multiplicative stable Lévy noise (an important class of non-Gaussian noise), by examining the qualitative changes of equilibrium states with its most probable phase portraits. We have found some peculiar bifurcation phenomena in contrast to the deterministic counterpart: (i) When the non-Gaussianity ...
Jinqiao Duan +3 more
arxiv +6 more sources
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.
Zhang, Jia-Fang, Zhang, Dan
doaj +5 more sources
Pitchfork Bifurcation In A Coupled Cell System [PDF]
arXivVarious 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.
Raj, Shikhar, Bose, Biplab
arxiv +5 more sources
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
semanticscholar +3 more sources
Pseudo-Pitchfork Bifurcation of Feasible Regions in Power Systems [PDF]
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2018 Local bifurcations occur in power systems, causing changes in power system dynamic behaviors. These local bifurcations include the saddle-node bifurcation, Hopf bifurcation, and structure-induced bifurcation. This paper presents a new type of bifurcation
Chu-Yang Jiang, H. Chiang
semanticscholar +2 more sources
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
semanticscholar +5 more sources
Universal Unfolding of Pitchfork Bifurcations and Shear-Band Formation in Rapid Granular Couette Flow [PDF]
arXiv, 2004 A numerical bifurcation analysis is carried out to understand the role of gravity on the shear-band formation in rapid granular Couette flow. At {\it low} shear rates, there is a unique solution with a {\it plug} near the bottom wall and a {\it shear-layer} near the top-wall; this solution mirrors typical shearbanding-type profiles in earth-bound shear-
Meheboob Alam
arxiv +3 more sources
The random dynamical pitchfork bifurcation with additive Lévy noises [PDF]
arXiv, 2022 This paper concerns the effects of additive non-Gaussian L\'evy noises on the pitchfork bifurcation. We consider two types of noises, $\alpha$-stable process and the truncated process. Under both $\alpha$-stable process and the truncated process, the classical pitchfork bifurcation model exists a unique invariant measure.
Ziying He, Xianming Liu
arxiv +3 more sources
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
openaire +4 more sources