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Showing 1 to 13 of 13 for “"Pitchfork bifurcation"”.
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Pitchfork bifurcations of invariant manifolds
… the system is said to have undergone a bifurcation. Bifurcations have been classified on the basis of the topological properties of fixed points and invariant manifolds of dynamical systems. A pitchfork bifurcation in R is said to have occurred when a stable fixed point becomes unstable …
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Investigation into the Local and Global Bifurcations of the Whirling Planar Pendulum
… dynamical system exhibits both local and global bifurcations. The local pitchfork bifurcation leads to the splitting of a single stable equilibrium point into three (two stable and one unstable), as the spin rate is increased. The global bifurcations lead to two independent types of chaotic …
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Analysis of solitary waves in inhomogeneous systems
… norm. In contrast to the symmetric case, pitchfork bifurcation no longer exists, and we find a saddle node one instead. For the second problem, we use coupled mode reduction method to yield conditions for symmetry breaking bifurcations. We notably obtain that the bifurcation is degenerate. …
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Biloba for chamber ensemble
… to different permutations of the plot of the pitchfork bifurcation equation in the supercritical case, which bears resemblance to the outline of a typical fan-shaped Gingko leaf. Aesthetically, the different levels of vibrationality of the sounds produced by the instruments were used to mirror …
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Computational Modeling of Superconductivity from the Set of Time-Dependent Ginzburg-Landau Equations for Advancements in Theory and Applications
… wire dynamics of phase slip centers (PSCs), the pitchfork bifurcation of PSC locations at varying energy gaps, the influence of phonon flux to the PSC, and the proposed application of a 1-D wire cryocooler from these previous results. The published result of the superconducting diode effect shows …
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On The Dynamics Of Systems With Vastly Different Frequencies
… For coupling strengths exceeding critical bifurcation values, the limit cycle of oscillator 1 or 2 is found to disappear. In the second problem, we consider a simple pendulum coupled to a horizontal mass-spring system of a much higher frequency. In contrast to the first problem, the …
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Hydraulics and instabilities of quasi-geostrophic zonal flows
… a range of beta. Multiple solutions arise at a pitchfork bifurcation as a stability parameter is raised above the stability threshold determined by the necessary condition for instability. The center branch of the pitchfork is unstable to the gravest mode, while the two outer branches do not …
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A theoretical and experimental investigation into the nonlinear dynamics of floating bodies
… of these equations are determined and their bifurcations are investigated. Hopf bifurcations are found. Numerical simulations are used to investigate the bifurcations of the ensuing limit cycles and how they produce chaos. Experiments are conducted with tanker and destroyer models. They …
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Problems in nonlinear dynamics
… be more than the number of linear normal modes. Bifurcations of the calculated nonlinear normal modes are investigated. For continuous systems without internal resonances, we consider a cantilever beam and compare two approaches for the determination of its nonlinear planar modes. In the first …
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Modal interactions in shell dynamics
… also undergo supercritical and subcritical Hopf bifurcations as the frequency or the amplitude of excitation varies. Between the two Hopf-bifurcation frequencies, the fixed-point solutions are unstable and limit cycles exist. Some limit cycles experience symmetry-breaking (pitchfork) bifurcation …
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Optically induced orientational transitions in nematic liquid crystals
… this state destabilizes via a supercritical Hopf bifurcation and a new frequency in the time Fourier spectra of the dynamical variables appears. This regime is quasiperiodic and corresponds to a precession and nutation of the director. As the intensity increases further, this state disappears at a …
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Electrohydrodynamic interactions of colloidal particles undergoing Quincke rotation
… the classic Lorenz oscillator equations with two bifurcations. When the applied electric field exceeds the critical electric field for spontaneous rotation, the angular velocity undergoes a supercritical pitchfork bifurcation, by which the zero angular velocity state becomes unstable and a stable …
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The Effect of Suspension on Parametric Stability and Bifurcation of Geared Systems in Permanent Contact Regime
Gears are known to be one of the most common mechanical parts used in rotary machinery and power transmission systems. Originally, gears are designed to remain in permanent contact regime, where the teeth in mesh do not separate during operation. But because of the clearance between the teeth in …