Cyclic symmetry induced pitchfork bifurcations in the diblock copolymer model [PDF]
Discrete and Continuous Dynamical Systems, Series B 29(2), pp.
666-701, 2024, 2022 The Ohta-Kawasaki model for diblock copolymers exhibits a rich equilibrium bifurcation structure. Even on one-dimensional base domains the bifurcation set is characterized by high levels of multi-stability and numerous secondary bifurcation points. Many of these bifurcations are of pitchfork type.
Peter Rizzi +2 more
arxiv +3 more sources
Stability analysis for pitchfork bifurcations of solitary waves in generalized nonlinear Schroedinger equations [PDF]
, 2012 Linear stability of both sign-definite (positive) and sign-indefinite solitary waves near pitchfork bifurcations is analyzed for the generalized nonlinear Schroedinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary ...
Akhmediev +34 more
core +2 more sources
Normal form for the symmetry-breaking bifurcation in the nonlinear Schrodinger equation [PDF]
arXiv, 2011 We derive and justify a normal form reduction of the nonlinear Schrodinger equation for a general pitchfork bifurcation of the symmetric bound state that occurs in a double-well symmetric potential.
Pelinovsky, Dmitry, Phan, Tuoc
core +2 more sources
Discretizing the transcritical and pitchfork bifurcations – conjugacy results [PDF]
Journal of Difference Equations and Applications, 2015 We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions on the one-step discretization method of order $p\ge 1$, we show that the time-$h$ exact and the step-size-$h$ discretized ...
Lajos Lóczi
+8 more sources
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.
Hou, Xiaojie, Korman, Philip, Li, Yi
openaire +2 more sources
The effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems [PDF]
Journal of Physics A: Mathematical and Theoretical, 2007 LaTex, 25 pp., 14 Figures (26 *.eps files); final version 3, to be published in Journal of Physics ...
Ayumu Sugita +3 more
openaire +4 more sources
Pitchfork and Hopf bifurcation thresholds in stochastic equations with delayed feedback [PDF]
Physical Review E, 2009 The bifurcation diagram of a model stochastic differential equation with delayed feedback is presented. We are motivated by recent research on stochastic effects in models of transcriptional gene regulation. We start from the normal form for a pitchfork bifurcation, and add multiplicative or parametric noise and linear delayed feedback.
Mathieu Gaudreault +2 more
openaire +5 more sources
On the effect of multiplicative noise in a supercritical pitchfork bifurcation
, 2010 The most important characteristic of {\em multiplicative noise} is that its effects of system's dynamics depends on the recent system's state. Consideration of multiplicative noise on self-referential systems including biological and economical systems therefore is of importance. In this note we study an elementary example.
Stefan Reimann
openaire +4 more sources
Pitchfork bifurcation and heteroclinic connections in the Kuramoto–Sivashinsky PDE
Journal of Computational DynamicsWe present a method for the complete analysis of the dynamics of dissipative Partial Differential Equations (PDEs) undergoing a pitchfork bifurcation. We apply our technique to the Kuramoto--Sivashinsky PDE on the line to obtain a computer-assisted proof of the creation of two symmetric branches of non-symmetric fixed points and heteroclinic ...
Kubica, Jacek +2 more
openaire +3 more sources
In vitro arrhythmia generation by mild hypothermia: a pitchfork bifurcation type process
Physiological Measurement, 2015 Binbin Xu +5 more
semanticscholar +4 more sources