Bifurcation Phenomena (bifurcation + phenomenon)

Distribution by Scientific Domains
Engineering75%

Selected Abstracts

Numerical implementation of Aristov,Pukhnachev's formulation for axisymmetric viscous incompressible flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2010
N. P. Moshkin
Abstract In the present work a finite-difference technique is developed for the implementation of a new method proposed by Aristov and Pukhnachev (Doklady Phys. 2004; 49(2):112,115) for modeling of the axisymmetric viscous incompressible fluid flows. A new function is introduced that is related to the pressure and a system similar to the vorticity/stream function formulation is derived for the cross-flow. This system is coupled to an equation for the azimuthal velocity component. The scheme and the algorithm treat the equations for the cross-flow as an inextricably coupled system, which allows one to satisfy two conditions for the stream function with no condition on the auxiliary function. The issue of singularity of the matrix is tackled by adding a small parameter in the boundary conditions. The scheme is thoroughly validated on grids with different resolutions. The new numerical tool is applied to the Taylor flow between concentric rotating cylinders when the upper and lower lids are allowed to rotate independently from the inner cylinder, while the outer cylinder is held at rest. The phenomenology of this flow is adequately represented by the numerical model, including the hysteresis that takes place near certain specific values of the Reynolds number. Thus, the present results can be construed to demonstrate the viability of the new model. The success can be attributed to the adequate physical nature of the auxiliary function. The proposed technique can be used in the future for in-depth investigations of the bifurcation phenomena in rotating flows. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Complex dynamics in one-dimensional CNNs

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 1 2006
István Petrás
Abstract The effect of boundary conditions on the global dynamics of cellular neural networks (CNNs) is investigated. As a case study one-dimensional template CNNs are considered. It is shown that if the off-diagonal template elements have opposite sign, then the boundary conditions behave as bifurcation parameters and can give rise to a very rich and complex dynamic behaviour. In particular, they determine the equilibrium point patterns, the transition from stability to instability and the occurrence of several bifurcation phenomena leading to strange and/or chaotic attractors and to the coexistence of several attractors. Then the influence of the number of cells on the global dynamics is studied, with particular reference to the occurrence of hyperchaotic behaviour. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Bifurcation behaviour in parallel-connected boost converters

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2001
H. H. C. Iu
Abstract This paper describes the bifurcation phenomena of a system of parallel-connected d.c./d.c. boost converters. The results provide important information for the design of stable current sharing in a master,slave configuration. Computer simulations and experiments are performed to capture the effects of variation of some chosen parameters on the qualitative behaviour of the system. In particular, it is found that variation of some parameters leads to Neimark,Sacker bifurcation. Analysis is presented to establish the possibility of the bifurcation phenomena. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Reduced model of discrete-time dynamic image segmentation system and its bifurcation analysis

INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 4 2009
Ken'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]