We show that the variation of topology at infinity a two-variable polynomial function is localisable finite number "atypical points" infinity. construct an effective algorithm with low complexity in order to detect sharply bifurcation values function.

this paper is devoted to study of a partial differential equation governing panel motion in supersonic flow. this pde can be transformed to an ode by means of a galerkin method. here by using a criterion which is closely related to the routh-hurwitz criterion, we investigate the mentioned transformed ode from hopf bifurcation point of view. in fact we obtain a region for existence of simple hop...

An adaptive oligopoly model, where the demand function is isoelastic and the competitors operate under constant marginal costs, is considered. The Cournot equilibrium point then loses stability through a subcritical Neimark bifurcation. The present paper focuses some global bifurcations, which precede the Neimark bifurcation, and produce other attractors which coexist with the still attractive ...

Box-models are important for qualitative description of thermohaline circulation. Their bifurcation analysis helps to understand possible mechanisms for the loss of stability. So far, bifurcations in box-models have been studied numerically, except for the saddle-node bifurcation in the Stommel type models. We consider a box-model with turbulent fluxes. We prove that a rapid growth of the trans...

The bifurcation sets of polynomial functions have been studied by many mathematicians from various points view. In particular, Némethi and Zaharia described them in terms Newton polytopes. this paper, we will show analogous results for rational functions.

We construct a large class of dynamically defined Cantor sets on the real line whose self-difference sets are Cantor sets of arbitrary positive measure. This relates to a question posed by J. Palis which arises naturally in the context of homoclinic bifurcations in dimension 2. §