Constructing global bifurcation diagrams by the parametric representation method

Application of the parametric representation method to construct bifurcation diagrams for highly non-linear chemical dynamical systems

The parametric representation method has been shown to be a useful geometric tool to study tangent and Hopf bifurcations in chemical systems. As an example, we investigate the behaviour of a two-dimensional system of differential equations. This general model includes some known catalytic oxidation models as special cases. The general system can have one or three stationary solutions depending ...

Hierarchical Dictionary Constructing Method for the Parametric Eigenspace Method

The parametric eigenspace method is an object recognition method based on visual learning approach with image coding technique. In this paper, to improve matching efficiency, a novel approach to construct hierarchical dictionary for the parametric eigenspace method is proposed. In the proposed constructing method, learning image set is classified hierarchically, and tree-structured dictionary i...

Constructing Colorings for Diagrams

Constructing parametric quadratic curves

Constructing a parametric spline curve to pass through a set of data points requires assigning a knot to each data point. In this paper we discuss the construction of parametric quadratic splines and present a method to assign knots to a set of planar data points. The assigned knots are invariant under a ne transformations of the data points, and can be used to construct a parametric quadratic ...

Global analysis of the nonlinear Duffing-van der Pol type equation by a bifurcation theory and complete bifurcation groups method

The work is devoted to the systematic research of the periodic, quasi-periodic or chaotic oscillations and the coexistence in the nonlinear Duffing-van der Pol type dynamical systems describing processes and phenomena in nature or engineering. The achieved result is the elaboration of the basic theory for searching nonlinear effects based on the concepts of periodic skeletons, bifurcation theor...