Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 67 for “"Hopf Bifurcation"”.
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Equivariant Global Hopf Bifurcation in Abstract Nonlinear Parabolic Equations
… this Thesis, we study local and global symmetric Hopf bifurcation in abstract parabolic systems by means of the twisted equivariant degree.
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On the stability of rotor bearing systems based on Hopf bifurcation theory
… turbulent effects are evaluated by applying the Hopf bifurcation theory (HBT) to the equations of motion. A method is developed for predicting the stability envelope of rotor-bearing systems using HBT. Results are compared with published literature obtained using a trial-and-error method. A …
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BIFDE: a numerical software package for the hopf bifurcation problem in functional differential equations
… software package has been written to compute the Hopf bifurcation structure in functional differential equations. The package is modular, and consists of several routines which perform one or more tasks. In conjunction with the routines available in this package, the user is required to provide a …
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Periodic Delay Effects on Cutting Tool Dynamics
… it is assumed that the delay equation exhibits a Hopf bifurcation when its delay Is unperturbed. The periodically perturbed system exhibits more delicate bifurcations than a Hopf bifurcation. We show that these bifurcations are well explained by the Bogdanov-Takens bifurcations when the ration …
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Application of Bifurcation Theory to Subsynchronous Resonance in Power Systems
A bifurcation analysis is used to investigate the complex dynamics of two heavily loaded single-machine-infinite-busbar power systems modeling the characteristics of the BOARDMAN generator with respect to the rest of the North-Western American Power System and the CHOLLA# generator with respect to …
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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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Dynamic Instabilities in Structures with Nonholonomic Constraints
… dynamics are analyzed within the framework of bifurcation and stability theory. Initially, the stability of Ziegler's double pendulum is analyzed to show its interesting dynamic behavior and capability of flutter via a Hopf bifurcation. The main contribution of the thesis is the development of …
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Sir epidemic and predator - prey models of fractional-order
… models were analyzed. Furthermore, the Hopf bifurcation analysis of each model was investigated . The result obtained showed that the model undergo Hopf bifurcation for some values. Throughout the project, the Adams-type predictor-corrector method to obtain the numerical solutions of the …
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Localised solutions of the parametrically driven Ginzburg-Landau and nonlinear Schrӧdinger equations
… amplitude equation for the modes excited near a Hopf bifurcation.
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Tuning of the Active Hair Bundle
… its parameters from experiment. We delineate the bifurcation structure of this simplified model, and analyse by perturbation methods its behavior in various dynamical regimes, notably in the relaxation-oscillation regime that displays prominently the hair bundle's active process; and in the …
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Tumour growth model of cancer self-remission with hassell-varley functional response
… Dimensional analysis, stability analysis and bifurcation analysis are used to analyse the model. Under certain condition, our numerical analysis showed an existence of Hopf-bifurcation for some parameter ranges, which generate periodic solution.
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Integrability, localisation and bifurcation of an elastic conducting rod in a uniform magnetic field
… methods. The rods buckle in a Hamiltonian-Hopf bifurcation about a periodic solution. A codimension-two point, which describes a double Hamiltonian-Hopf bifurcation, determines whether straight rods buckle into localised configurations at either two critical values of the magnetic field, a …
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Dynamics of power systems at critical load levels
… dynamic nature of the voltage problem. Finally, Hopf bifurcation theory has been used to analyze the nonlinear power system at critical load levels.
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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 …
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Studies of Vortex Breakdown and its Stability in a Confined Cylindrical Container
… mode competition in the neighborhood of a double Hopf point, our experiments provide, for the first time, the laboratory evidence of the existence of an axisymmetric double Hopf bifurcation, involving the competition between two coexisting axisymmetric stable limit cycles. For the study of …
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Modal interactions in the dynamic response of isotropic and composite plates
… the fixed points lose stability via a Hopf bifurcation, thereby giving rise to limit cycle solutions. It is shown that these limit-cycles undergo a series of period-doubling bifurcations, culminating in chaos. Finally, the case of a combination resonance involving the first three modes …
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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 …
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Mathematical Models of Biochemical Oscillations
… oscillatory behavior. The importance of the Hopf Bifurcation will be discussed in detail for the central role it plays in limit cycle behavior and instability. Once we have exposed the necessary mathematical framework, we consider several specific models of biochemical oscillators in three or …
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Mechanical Control of Sensory Hair-Bundle Function
… essential similarity between hair bundles. The bifurcation near which a bundle's operating point resides controls its function: the state diagram provides a functional map of mechanosensory modalities. Auditory function is best tuned near a supercritical Hopf bifurcation, whereas vestibular …
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Population Dynamics and Pattern Formation in an Info-chemical Mediated Tri-trophic Plankton Model
… the degenerated situation wherein Turing bifurcation and Hopf bifurcation occur simultaneously. We also consider under what conditions Turing patterns are exhibited and under what conditions spatiotemporal patterns are observed generally. The Transient Turing instability of spatial …
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