Let Riemannian metrics g and ḡ on a connected manifold Mn have the same geodesics (considered as unparameterized curves). Suppose the eigenvalues of one metric with respect to the other are all different at a point. Then, by the famous Levi-Civita’s Theorem, the metrics have a certain standard form near the point. Our main result is a generalization of Levi-Civita’s Theorem for the points where...

The results for blood flow in the carotid artery bifurcation on the basis of numerical simulation of Navier-Stokes equations are presented in this study. Four cases of carotid bifurcation are considered: common carotid artery (CCA) bifurcation without stenoses and cases with one, two and three stenoses are also presented. The results are obtained by performing numerical simulations considering ...

In this paper a biometric system for personal identification, realized through the manipulation of retinal fundus images and the detection of its bifurcation points, is described. In the image pre-processing step, a strong contrast exaltation between blood vessels and the background in retinal image is carried out; then blood vessels are extracted and next the vasculature bifurcation and crosso...

We explore the singularity-induced bifurcation and singular Hopf bifurcation theorems and the degeneracies that arise when Newton’s Laws are coupled to Kirchhoff’s Laws. Such models are used in the electrical engineering literature to describe electrical power systems and they can take the form of either an index-1 differential-algebraic equation (DAE) or a singularly perturbed ordinary differe...

In this paper, we numerically investigate local properties of dynamical systems close to a Hopf bifurcation instability. We focus on chemical systems and present an approach based on the theory of normal forms for determining numerical estimates of the limit cycle that branches off at the Hopf bifurcation point. For several numerically ill-conditioned examples taken from chemical kinetics, we c...

This paper is concerned with the analysis of two-parameter bifurcation phenomena in the buck power converter. It is shown that the complex dynamics of the converter can be unfolded by considering higher codimension bifurcation points in two-parameter space. Specifically, standard smooth bifurcations are shown to merge with discontinuity-induced bifurcation (DIB) curves, giving rise to intricate...

We show in this paper how numerical bifurcation analysis can be used to study the evolution of genetically transmitted phenotypic traits. For this, we consider the standard Rosenzweig-MacArthur prey-predator model and, following the so-called Adaptive Dynamics approach, we derive from it a second-order evolutionary model composed of two ODEs, one for the prey trait and one for the predator trai...

OBJECTIVE To demonstrate the bifurcation pattern of the tibial nerve and its branches. METHODS Eleven legs of seven fresh cadavers were dissected. The reference line for the bifurcation point of tibial nerve branches was an imaginary horizontal line passing the tip of the medial malleolus. The distances between the reference line and the bifurcation points were measured. The bifurcation branc...

In this paper, the Poincaré map function as a one-dimensional first-return map is obtained by approximating the scatter plots of inter-peak interval (IPI) during preictal and postictal periods from invasive EEG recordings of nine patients suffering from medically intractable focal epilepsy. Evolutionary Algorithm (EA) is utilized for parameter estimation of the Poincaré map. Bifurcation analyse...