Bifurcation of critical periods of a quartic system

For the polynomial system x˙ = ix + xx¯(ax2 + bxx¯ + cx¯ 2 ) the study of critical period bifurcations is performed. Using calculations with algorithms of computational commutative algebra it is shown that at most two critical periods can bifurcate from any nonlinear center of the system

Bifurcation of critical periods of a quartic system

For the polynomial system x˙ = ix + xx¯(ax2 + bxx¯ + cx¯ 2 ) the study of critical period bifurcations is performed. Using calculations with algorithms of computational commutative algebra it is shown that at most two critical periods can bifurcate from any nonlinear center of the system

Analysis of the Discrete Theory of Radiative Transfer in the Coupled "Ocean-Atmosphere" System: Current Status, Problems and Development Prospects

In this paper, we analyze the current state of the discrete theory of radiative transfer. One-dimensional, three-dimensional and stochastic radiative transfer models are considered. It is shown that the discrete theory provides a unique solution to the one-dimensional radiative transfer equation. All approximate solution techniques based on the discrete ordinate formalism can be derived based on the synthetic iterations, the small-angle approximation, and the matrix operator method. The possible directions for the perspective development of radiative transfer are outlined

Linearization of two-dimensional systems of ODEs without conditions on small denominators

We study the problem of linearizability for two-dimensional systems of ODEs in a neighborhood of the saddle type singular point with rationally incommensurable eigenvalues. It is shown that if the linearizing transformation is convergent in one of the variables, then it is absolutely convergent

MARKET NICHE, FLEXIBILITY AND COMMITMENT

We study a market-entry game in which the potential entrants wish to coordinate their actions (i.e. enter different market segments rather than compete directly). If (i) the firms have an option to wait, and (ii) each firm has a different reaction time after they have decided to wait, the unique outcome that survives the iterated elimination of weakly dominated strategies favors the less flexible firms. Copyright � 2007 The Authors; Journal compilation � 2007 Blackwell Publishing Ltd and The University of Manchester.