A numerical tool for the detection of degenerated symmetry breaking bifurcation points is presented. The degeneracies are classified and numerically processed on 1-D restrictions of the bifurcation equation. The test functions that characterise each of the equivalence classes are constructed by means of an equivariant numerical version of the Liapunov-Schmidt reduction. The classification suppl...

Lorenz like attractors are known to appear in unfoldings from certain codimension two homoclinic bifurcations for differential equations in R that possess a reflectional symmetry. This includes homoclinic loops under a resonance condition and the inclination flip homoclinic loops. We show that Lorenz like attractors also appear in the third possible codimension two homoclinic bifurcation (for h...

This paper is devoted to the study of a spatially and age structured population dynamics model. We study the stability and Hopf bifurcation of the positive equilibrium of the model by using a bifurcation theory in the context of integrated semigroups. This problem is a first example for Hopf bifurcation for a spatially and age/size structured population dynamics model. Bifurcation analysis indi...

In this paper, applying frequency domain approach, a delayed competitive web-site system is investigated. By choosing the parameter α as a bifurcation parameter, it is found that Hopf bifurcation occurs as the bifurcation parameter α passes a critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some nume...

A dangerous border collision bifurcation has been defined as the dynamical instability that occurs when the basins of attraction of stable fixed points shrink to a set of zero measure as the parameter approaches the bifurcation value from either side. This results in almost all trajectories diverging off to infinity at the bifurcation point, despite the eigenvalues of the fixed points before an...

INTRODUCTION Treatment of wide-necked bifurcation aneurysms often poses procedural and long-term outcome challenges. The initial preclinical experience with the Pulsar Vascular Aneurysm Neck Reconstruction Device (PVANRD) in a canine bifurcation model is described. METHODS Experimental bifurcation vein pouch aneurysms were surgically created in the carotid arteries of eight dogs. Endovascular...

Abstract—The Nagumo-Sato model is one of mathematical neuron models described by a piecewise linear difference equation. Since there is a conditional character which is discontinuous at the threshold value, the system can be classified as a hybrid dynamical system. Bifurcation phenomena are occurred by changing internal parameters and chaotic attractors are also given. The dynamical properties ...

‎In this paper‎, ‎first we discuss a local stability analysis of model was introduced by P‎. ‎J‎. ‎Mumby et‎. ‎al‎. ‎(2007)‎, ‎with $frac{gM^{2}}{M+T}$ as the functional response term‎. ‎We conclude that the grazing intensity is the important parameter to control the existence or extinction of the coral reef‎. ‎Next‎, ‎we consider this model under the influence of the time delay as the bifurcat...

The network equations of electric power system are formed in which the node voltages and branch currents are as state variables by π equivalent circuit simulation of power components. The explicit expressions of power system voltage equilibrium solution curves are obtained by solving the equations above, and then get the characteristic equation of the saddle-node bifurcation point, define the f...