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Computing multiple pitchfork bifurcation points
Computing, 1997For the parameter dependent nonlinear equation \(F(x,\lambda) =0\), \(F: \mathbb{R}^n \times \mathbb{R}^1 \to\mathbb{R}^n\), the generically important case \(\text{rank} \partial_x E(x^*, \lambda^*) =n-1\) is investigated. In a neighborhood of such pitchfork bifurcation point \((x^*, \lambda^*)\) of multiplicity \(p\geq 1\) the Lyapunov-Schmidt ...
Pönisch, G. +2 more
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A pitchfork bifurcation in the tatonnement process ★ [PDF]
Economic Theory, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A REMARK ON HETEROCLINIC BIFURCATIONS NEAR STEADY STATE/PITCHFORK BIFURCATIONS
International Journal of Bifurcation and Chaos, 2004We consider a bifurcation that occurs in some two-dimensional vector fields, namely a codimension-one bifurcation in which there is simultaneously the creation of a pair of equilibria via a steady state bifurcation and the destruction of a large amplitude periodic orbit.
Kirk, Vivien, Knobloch, Edgar
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Control of Pitchfork and Hopf Bifurcations
1992 American Control Conference, 1992A multiple-scale analysis is used to determine the effect of a linear regulator with a small gain on systems which exhibit pitchfork or Hopf bifurcations in open loop.
E. Henrich, D. Mingori, P. Monkewitz
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Time-reversible and equivariant pitchfork bifurcation
Physica D: Nonlinear Phenomena, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lim, Chjan C., Mccomb, I-Heng
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Spectral signature of the pitchfork bifurcation: Liouville equation approach
Physical Review E, 1995The time evolution of probability densities of one-dimensional nonlinear vector fields is studied using a Liouville equation approach. It is shown that the Liouville operator admits a discrete spectrum of eigenvalues of decaying type if the vector field is far from bifurcation.
Gaspard, Pierre +3 more
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Parametric small signal amplification near pitchfork bifurcations
Ferroelectrics, 1995Abstract The nonlinear dielectric properties of ferroelectrics during polarization reversal are used to amplify small periodic perturbations. The ferroelectric serves as a nonlinear capacitor in a series-resonance circuit. The inductance is a linear one.
Martin Diestelhorst +2 more
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Interactions of Hopf and Pitchfork Bifurcations
1980Non linear interactions between a Hopf bifurcation and a pitchfork-type stationary bifurcation can produce secondary bifurcations of periodic solutions, and tertiary bifurcations of periodic or aperiodic solutions lying on an invariant torus. A complete classification of the resulting bifurcation diagrams is presented, with emphasis on the cases which ...
W. F. Langford, G. Iooss
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Pseudo-Pitchfork Bifurcation of Feasible Regions in Power Systems
International Journal of Bifurcation and Chaos, 2018Local 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 that can occur in the optimal power flow (OPF) problem.
Chu-Yang Jiang, Hsiao-Dong Chiang
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Sensitivity of pitchfork bifurcation to stochastic perturbation
Dynamics and Stability of Systems, 1992For a stochastically perturbed two-dimensional system exhibiting a pitchfork bifurcation, asymptotic expansions for the Lyapunov exponent and the rotation number are obtained in the vicinity of the point of deterministic bifurcation. Using the result for the Lyapunov exponent, the shift in the bifurcation point due to the stochastic perturbation is ...
S. T. Ariaratnam, Wei-Chau Xie
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