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Bifurcation Analysis (bifurcation + analysis)
Selected AbstractsBifurcation analysis of a piecewise smooth system with non-linear characteristicsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 4 2005Takuji Kousaka Abstract In previous works, there are no results about the bifurcation analysis for a piecewise smooth system with non-linear characteristics. The main purpose of this study is to calculate the bifurcation sets for a piecewise smooth system with non-linear characteristics. We first propose a new method to track the bifurcation sets in the system. This method derives the composite discrete mapping, Poincaré mapping. As a result, it is possible to obtain the local bifurcation values in the parameter plane. As an illustrated example, we then apply this general methodology to the Rayleigh-type oscillator containing a state- period-dependent switch. In the circuit, we can find many subharmonic bifurcation sets including global bifurcations. We also show the bifurcation sets for the border-collision bifurcations. Some theoretical results are verified by laboratory experiments. Copyright © 2005 John Wiley & Sons, Ltd. [source] Analysis of critical motions of floating structuresPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Marc-André Pick Validation of numerical methods for describing the motion of a ship in sea conditions by adequate experiments is a major research field in ocean engineering. For the development of a method for the systematic determination of critical and safe operational conditions and for the classification of capsize scenarios bifurcation analyses are performed. The computational effort for these analyses is enormous using a full model describing the nonlinear dynamics of a floating body. Therefore, a method for model reduction is currently being developed at the Institute of Mechanics and Ocean Engineering at TUHH. Bases for the validation of this new method are experiments conducted in the institute's wave tank. The determination of position and attitude of the body is performed with an integrated measurement system: An inertial measurement unit and a video system are combined using an extended Kalman Filter. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A population-based model of the nonlinear dynamics of the thalamocortical feedback network displays intrinsic oscillations in the spindling (7,14 Hz) rangeEUROPEAN JOURNAL OF NEUROSCIENCE, Issue 12 2005Nada A. B. Yousif Abstract The thalamocortical network is modelled using the Wilson,Cowan equations for neuronal population activity. We show that this population model with biologically derived parameters possesses intrinsic nonlinear oscillatory dynamics, and that the frequency of oscillation lies within the spindle range. Spindle oscillations are an early sleep oscillation characterized by high-frequency bursts of action potentials followed by a period of quiescence, at a frequency of 7,14 Hz. Spindles are generally regarded as being generated by intrathalamic circuitry, as decorticated thalamic slices and the isolated thalamic reticular nucleus exhibit spindles. However, the role of cortical feedback has been shown to regulate and synchronize the oscillation. Previous modelling studies have mainly used conductance-based models and hence the mechanism relied upon the inclusion of ionic currents, particularly the T-type calcium current. Here we demonstrate that spindle-frequency oscillatory activity can also arise from the nonlinear dynamics of the thalamocortical circuit, and we use bifurcation analysis to examine the robustness of this oscillation in terms of the functional range of the parameters used in the model. The results suggest that the thalamocortical circuit has intrinsic nonlinear population dynamics which are capable of providing robust support for oscillatory activity within the frequency range of spindle oscillations. [source] Micromechanical analysis of failure propagation in frictional granular materialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2009Antoinette Tordesillas Abstract The extent to which the evolution of instabilities and failure across multiple length scales can be reproduced with the aid of a bifurcation analysis is examined. We adopt an elastoplastic micropolar constitutive model, recently developed for dense cohesionless granular materials within the framework of thermomicromechanics. The internal variables and their evolution laws are conceived from a direct consideration of the dissipative mechanism of force chain buckling. The resulting constitutive law is cast entirely in terms of the particle scale properties. It thus presents a unique opportunity to test the potential of micromechanical continuum formulations to reproduce key stages in the deformation history: the development of material instabilities and failure following an initially homogeneous deformation. Progression of failure, initiating from frictional sliding and rolling at contacts, followed by the buckling of force chains, through to macroscopic strain softening and shear banding, is reproduced. Bifurcation point, marking the onset of shear banding, occurred shortly after the peak stress ratio. A wide range of material parameters was examined to show the effect of particle scale properties on the progression of failure. Model predictions on the thickness and angle of inclination of the shear band and the structural evolution inside the band, namely the latitudinal distribution of particle rotations and the angular distributions of contacts and the normal contact forces, are consistent with observations from numerical simulations and experiments. Copyright © 2009 John Wiley & Sons, Ltd. [source] Bifurcation modeling in geomaterials: From the second-order work criterion to spectral analysesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2009F. Prunier Abstract The present paper investigates bifurcation analysis based on the second-order work criterion, in the framework of rate-independent constitutive models and rate-independent boundary-value problems. The approach applies mainly to nonassociated materials such as soils, rocks, and concretes. The bifurcation analysis usually performed at the material point level is extended to quasi-static boundary-value problems, by considering the stiffness matrix arising from finite element discretization. Lyapunov's definition of stability (Annales de la faculté des sciences de Toulouse 1907; 9:203,274), as well as definitions of bifurcation criteria (Rice's localization criterion (Theoretical and Applied Mechanics. Fourteenth IUTAM Congress, Amsterdam, 1976; 207,220) and the plasticity limit criterion are revived in order to clarify the application field of the second-order work criterion and to contrast these criteria. The first part of this paper analyses the second-order work criterion at the material point level. The bifurcation domain is presented in the 3D stress space as well as 3D cones of unstable loading directions for an incrementally nonlinear constitutive model. The relevance of this criterion, when the nonlinear constitutive model is expressed in the classical form (d, = Md,) or in the dual form (d, = Nd,), is discussed. In the second part, the analysis is extended to the boundary-value problems in quasi-static conditions. Nonlinear finite element computations are performed and the global tangent stiffness matrix is analyzed. For several examples, the eigenvector associated with the first vanishing eigenvalue of the symmetrical part of the stiffness matrix gives an accurate estimation of the failure mode in the homogeneous and nonhomogeneous boundary-value problem. Copyright © 2008 John Wiley & Sons, Ltd. [source] The buckling mode extracted from the LDLT -decomposed large-order stiffness matrixINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2002Fumio Fujii Abstract The present study proposes an innovated eigenanalysis-free idea to extract the buckling mode only from the LDLT -decomposed stiffness matrix in large-scale bifurcation analysis. The computational cost for extracting the critical eigenvector is negligible, because the decomposition of the stiffness matrix will continually be repeated during path-tracing to solve the stiffness equations. A numerical example is computed to illustrate that the proposed idea is tough enough even for multiple bifurcation. Copyright © 2002 John Wiley & Sons, Ltd. [source] Bifurcation analysis of a piecewise smooth system with non-linear characteristicsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 4 2005Takuji Kousaka Abstract In previous works, there are no results about the bifurcation analysis for a piecewise smooth system with non-linear characteristics. The main purpose of this study is to calculate the bifurcation sets for a piecewise smooth system with non-linear characteristics. We first propose a new method to track the bifurcation sets in the system. This method derives the composite discrete mapping, Poincaré mapping. As a result, it is possible to obtain the local bifurcation values in the parameter plane. As an illustrated example, we then apply this general methodology to the Rayleigh-type oscillator containing a state- period-dependent switch. In the circuit, we can find many subharmonic bifurcation sets including global bifurcations. We also show the bifurcation sets for the border-collision bifurcations. Some theoretical results are verified by laboratory experiments. Copyright © 2005 John Wiley & Sons, Ltd. [source] Reduced model of discrete-time dynamic image segmentation system and its bifurcation analysisINTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 4 2009Ken'ichi Fujimoto Abstract We have developed a discrete-time dynamic image segmentation system consisting of chaotic neurons and a global inhibitor. Our system receives an image with isolated regions and can output segmented images in time series based on oscillatory responses of chaotic neurons. In this article, we derive a reduced model to find intrinsic properties of the system of dynamic image segmentation. Using numerical method for analyzing dynamical systems, we investigated bifurcation phenomena of a fixed point observed in the reduced model. As the results, in a model of two coupled chaotic neurons, we found that a set of Neimark-Sacker bifurcations causes the generation of an in-phase oscillatory response, which is unsuitable for the purpose of dynamic image segmentation. The bifurcation analysis gives appropriate parameter values to exclude the generation of in-phase oscillatory responses, i.e., our dynamic image segmentation system can work well. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 283,289, 2009 [source] Generalization and numerical investigation of QMOMAICHE JOURNAL, Issue 1 2007R. Grosch Abstract A generalized framework is developed for the quadrature method of moments (QMOM), which is a solution method for population balance models. It further evaluates the applicability of this method to industrial suspension crystallization processes. The framework is based on the concepts of generalized moments and coordinate transformations, which have been used already in earlier solution approaches. It is shown how existing approaches to QMOM are derived from the suggested unified framework. Thus, similarities and differences between the various QMOM methods are uncovered. Further, potential error sources involved in the different approaches to QMOM are discussed and assessed by means of a series of test cases. The test cases are selected to be challenging. The error in the QMOM solution is evaluated by comparison to an adaptive, error controlled solution of the population balance. The behavior of a range of different QMOM formulations is analyzed by means of numerical quadrature, dynamic simulation, as well as numerical continuation and bifurcation analysis. As a result of this detailed analysis, some general limitations of the method are detected and guidelines for its application are developed. This article is limited to lumped population balance models with one internal coordinate. © 2006 American Institute of Chemical Engineers AIChE J, 2007 [source] Global and local linear buckling behavior of a chiral cellular structurePHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 3 2005A. Spadoni Abstract This paper investigates the flat-wise compression behavior of an innovative cellular structure configuration. The considered layout has a hexagonal chiral geometry featuring cylinders, or nodes, joined by ligaments, or ribs. The resulting assembly is characterized by a number of interesting properties that can be exploited for the design of alternative honeycombs or cellular topologies to be used in sandwich construction. The flat-wise strength of the chiral geometry is investigated through classical analytical formulas for the linear buckling of thin plates and shells and a bifurcation analysis performed on a Finite Element model. The analytical expressions predict the global buckling behavior and the resulting critical loads, and can be directly compared with the results obtained from the Finite Element analysis. In addition, the Finite Element model predicts local buckling modes, which should be considered to evaluate the possible development of localized plasticity. A sensitivity study is performed to evaluate the influence of the geometry of the chiral structure on its buckling strength. The study shows that the considered topology can offer great design flexibility, whereby several parameters can be selected and modified to improve the flat-wise performance. The comparison with traditional, hexagonal centro-symmetric structural configurations concludes the paper and demonstrates the enhanced performance and the potentials of chiral noncentro-symmetric designs. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||