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Showing 1 to 20 of 175 for “"Bifurcations"”.
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Pitchfork bifurcations of invariant manifolds
… 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 and two new …
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Hamiltonian bifurcations in Schrodinger trimers
… whose topologies change due to Hamiltonian Hopf bifurcations and transcritical bifurcations. The Hamiltonian Hopf bifurcation occurs when eigenvalues on the imaginary axis collide and split and has two types: elliptic and hyperbolic. These two types arise in the DNLS problem, and the families of …
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Bifurcations of maps: numerical algorithms and applications
… obtain a global picture of the system. At local bifurcations, the number of steady states can change, or the stability properties of a steady state may change. The computational analysis of local bifurcations usually begins with an attempt to compute the coefficients that appear in the normal …
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River bifurcations: key processes, timescales and evolutionary trajectories
River bifurcations are constituent components of multi-thread fluvial systems, playing a crucial role in their morphodynamic evolution. As highlighted by several field studies and laboratory investigations, natural bifurcations tend to display unbalanced configurations, in which one branch carries …
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Global bifurcations and chaos in nonlinear mechanical systems
The local and global bifurcation behavior of various structural and mechanical systems have been examined in detail. The analysis is divided into three main parts. In the first part, global bifurcation analysis is performed for externally excited nonlinear systems with initial imperfections and a …
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Bifurcations, Multi-stability, and Localization in Thin Structures
… experimentally explores the multi-stability and bifurcations of buckled elastic strips subject to clamping and lateral end translations, and compares these results with numerical continuation of a perfectly anisotropic Kirchhoff rod model. It is shown that this naive Kirchhoff rod model works …
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Hopf bifurcations in magnetoconvection in the presence of sidewalls
We study multiple Hopf bifurcations that occur in a model of a layer of a viscous, electrically conducting fluid that is heated from below in the presence of a. magnetic field. We assume that the fluid flow is two-dimensional, and consider the effects of sidewalls with stress-free boundary …
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Hopf Bifurcations and Horseshoes Especially Applied to the Brusselator
In this paper we explore bifurcations, in particular the Hopf bifurcation. We study this especially in connection with the Brusselator, which is a model of certain chemical reaction-diffusion systems. After a thorough exploration of what a bifurcation is and what classifications there are, we give …
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Stochastic stability and global bifurcations in gyroscopic mechanical systems
The stability and bifurcation behavior of mechanical systems parametrically excited by small periodic or stochastic perturbations is studied. In the case of random excitation, the almost-sure and moment asymptotic stability of two- and four-dimensional dynamical systems subject to small intensity …
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Bifurcations in nonlinear Schrödinger equations with double well potentials
… and repelling nonlinearities. We discuss bifurcations along bound states, especially ground states and the first excited states, and also deal with orbital stability of the ground states. In attractive case with large separations for double wells, our results shows that the ground state …
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Multiple steady solutions and bifurcations in the symmetric driven cavity
… for higher Reynolds numbers. Subcritical bifurcations are observed for two-dimensional flow. Unsteady flow behavior occurs at higher Reynolds number. Three-dimensional simulations for a cube show only one steady solution.</p>
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Formation of branching angles at bifurcations of ant trail networks
… these trail networks. It has been observed, that bifurcations are symmetrical when moving from the nest to the food source, while are asymmetrical when moving back towards the nest. The mean bifurcation angles have been found to be 50 - 80 for networks radiating out from the nest. This thesis …
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Bifurcations of Parametrically Excited Gyroscopic Systems Near a 0 : 1 Resonance
… of this research involves study of the global bifurcations of the two gyroscopic systems. Using recently developed bifurcation methods, we detect the presence of multi-pulse orbits homoclinic to a slow manifold. In certain parameter regions, we can prove that multi-pulse orbits exist which are …
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Bifurcations in discrete-time neural networks : controlling complex network behaviour with inputs
… the solution manifolds of local fixed point bifurcations, i.e. saddle-node, flip and Neimark-Sacker bifurcations, a system of nonlinear equations is solved in two steps: First the bifurcation manifolds are derived in the intermediate space of activation function derivatives and second are …
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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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Bifurcations in the Echebarria-Karma Modulation Equation for Cardiac Alternans in One Dimension
… through an interesting series of secondary</p><p>bifurcations.</p><p>We also find that for some extreme range of parameters, the</p><p>modulation equation also includes chaotic solutions. Chaotic waves</p><p>in recent years has been regarded to be closely related with</p><p>dreadful cardiac …
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