17,518 research outputs found
Transversal conics and the existence of limit cycles
This paper deals with the problem of location and existence of limit cycles
for real planar polynomial differential systems. We provide a method to
construct Poincar\'e--Bendixson regions by using transversal conics. We present
several examples of known systems in the literature showing different features
about limit cycles: hyperbolicity, Hopf bifurcation, sky-blue bifurcation,
rotated vector fields, \ldots for which the obtained Poincar\'e--Bendixson
region allows to locate the limit cycles. Our method gives bounds for the
bifurcation values of parametrical families of planar vector fields and
intervals of existence of limit cycles.Comment: 28 pages; 20 figure
Zeros of the Partition Function and Pseudospinodals in Long-Range Ising Models
The relation between the zeros of the partition function and spinodal
critical points in Ising models with long-range interactions is investigated.
We find the spinodal is associated with the zeros of the partition function in
four-dimensional complex temperature/magnetic field space. The zeros approach
the real temperature/magnetic field plane as the range of interaction
increases.Comment: 20 pages, 9 figures, accepted to PR
- …