Conservative generalized bifurcation diagrams

Bifurcation Diagrams of Nonlinear RLC Electrical Circuits

This work investigates the application of bifurcation diagrams in the chaotic study of nonlinear RLC electrical circuits. The relevant second order differential equations were solved for ranges of appropriate parameters using Runge-Kutta approach. The solutions obtained were employed to produce bifurcation diagrams using Microsoft excel 2007. The mean estimate of 669 . 4   obtained from the b...

Discretizing bifurcation Diagrams Near codimension Two Singularities

We consider parameter-dependent, continuous-time dynamical systems under discretizations. It is shown that fold-Hopf singularities are O(h)-shifted and turned into fold-Neimark-Sacker points by one-step methods of order p. Then we analyze the effect of discretizations methods on the local bifurcation diagram near BogdanovTakens and fold-Hopf singularities. In particular we prove that the discre...

Bifurcation diagrams of coupled Schrödinger equations

Radially symmetric solutions of many important systems of partial differential equations can be reduced to systems of special ordinary differential equations. A numerical solver for initial value problems for such systems is developed based on Matlab, and numerical bifurcation diagrams are obtained according to the behavior of the solutions. Various bifurcation diagrams of coupled Schrödinger e...

Visualization of Generalized Voronoi Diagrams

Voronoi diagrams are an important data structure in computer science. However well studied mathematically, understanding such diagrams for different metrics, orders, and site shapes is a complex task. We propose a new method to visualize k-order diagrams and give an efficient adaptive implementation for this method. The algorithm is easy to customize for different metrics and site shapes. Its r...

Double zero bifurcation of non-linear viscoelastic beams under conservative and non-conservative loads