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Showing 1 to 18 of 18 for “"bifurcation diagram"”.
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Uncertainty in the Bifurcation Diagram of a Model of Heart Rhythm Dynamics
… parameter. Model dynamics was characterized with bifurcation analysis, which determines the APD and stability of fixed points of the model at a range of BCLs, and the BCLs at which bifurcations occur. These quantities can be plotted in a bifurcation diagram, which summarizes the dynamics of the …
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Mixing enhancement by dual speed rotating stirrer
… considered using dynamical systems theory. The bifurcation diagram reveals the presence of degenerate fixed points and homoclinic/heteroclinic orbits, whose nature varies for different parameter values. By considering an initially concentrated set of marker particles and using the various …
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Mathematical Models of the Alpha-Beta Phase Transition of Quartz
… on systems with hexagonal symmetry to derive the bifurcation diagram for Parlinski's model. Finally, we study a large class of modifications to Parlinski's model and show that all such modifications have the same bifurcation picture as the original model.
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Dynamics and Asymptotic Behavior of the Solutions of a Nonlinear Differential Equation
… produces a numerical solution which resembles a bifurcation diagram very similar to that produced by the logistic map. Comparisons of such numerical solutions to the logistic map are made, and a partial explanation of such numerical solutions is given. Then, the exact solution of the initial …
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A computer assisted approach to Hilbert's 16th problem
… 2, we describe multiparameter vectors, their bifurcations and rotated vector fields. In Chapter 3, we introduce parameter continuation methods and applications to multiparameter vectors. In Chapter 4, we summarize recent studies of quadratic systems and address the most used methods, including …
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Bifurcation Analysis of a Model of the Frog Egg Cell Cycle
… to the behavior of the model are provided by bifurcation theory, especially characterization of the codimension-1 and -2 bifurcation sets of the differential equations. To illustrate this method, I have been studying a system of 9 ordinary differential equations that describe the frog egg cell …
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Exploring global dynamics in a low order model of parallel shear flow
… flow that exhibits the phenomenon. We study the bifurcation diagram of a periodic solution of the Waleffe model found by the method of Nagata. Therein we find a codimension 2 bifurcation. The type of bifurcation, namely LPNS, ensures that we can find homoclinic and heteroclinic connections of …
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Nonlinear Dynamics of Tapping Mode Atomic Force Microscopy
… monostable and bistable regions of the static bifurcation diagram in the reference configuration. Free-vibration responses of the AFM probes, including the microcantilever natural frequencies and mode shapes, are determined. It is found that, for the parameters used in a practical operation of …
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Homoclinic snaking in discrete systems
… we investigate analytically and numerically bifurcations of localized solutions in discrete systems, i.e., the discrete Swift-Hohenberg, an optical cavity equation, and the discrete Allen-Cahn equation, which have infinitely multiplicity called homoclinic snaking. First, we study the discrete …
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Spatio-temporal dynamics before population collapse
… collapse. In the first project, we mapped the bifurcation diagram experimentally and found that the populations became more vulnerable to disturbance closer to the tipping point. Fluctuations of population density increased in size and timescale near the tipping point, in agreement with the …
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Stability of nonlinear oscillatory systems with application to ship dynamics
A procedure to generate an approximate bifurcation diagram for a single-degree-of-freedom system in a selected parameter space is developed. The procedure is based on the application of Floquet analysis to determine the stability of second-order perturbation approximations of the solutions of the …
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Constrained Buckling of Variable Length Elastica
… and (ii) the factors that define the bifurcation diagram. Two distinct classes of problems are analyzed; (i) the classical buckling problem of a constant length elastica and (ii) the insertion buckling problem of a variable length elastica. Their main difference is the generation of a …
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Nonlinear dynamics of a nematic liquid crystal in the presence of a shear flow
… shear rate, and by employing continuation and bifurcation theory we describe the different time dependent states for the two and three dimensional cases.<br/><br/>For the two dimensional case we compute the steady state solution branches finding that the flow favours an in-plane nematic state …
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Dynamical systems and their applications in neuroscience
… for the study of dynamical systems and their bifurcations, are explained: the user can compute the PRC of a limit cycle and its derivative, he can detect and continue homoclinic bifurcations, initiate these curves from different bifurcations and detect many codim 2 bifurcations on these …
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Studies on quasicrystals, superconducting micronetworks, and Josephson junction arrays
… provides a systematic method of obtaining the bifurcation diagram of the energy spectra and the magnitude of the energy level splittings. Our results are very general and apply to both diagonal and off-diagonal quasiperiodicity. The second part of this thesis deals with analytical calculations …
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A theoretical and experimental investigation of parametrically excited nonlinear mechanical systems
… The analogue computer is used to generate a bifurcation diagram in the excitation amplitude versus excitation frequency domain. The digital computer is used to obtain Poincare maps of strange attractors, to investigate larger amplitude responses, and to show the transition to a fractal basin …
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Dynamics of a Q-switched all-fibre laser
… observed dynamics are interpreted in terms of bifurcations of equilibria and periodic orbits. Specifically, we examine the coefficient of absorption of the Thulium doped fibre and study how the efficiency of its saturation depends on the physical length of the absorber section that initiates …
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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 …