382 research outputs found
Superstable cycles for antiferromagnetic Q-state Potts and three-site interaction Ising models on recursive lattices
We consider the superstable cycles of the Q-state Potts (QSP) and the
three-site interaction antiferromagnetic Ising (TSAI) models on recursive
lattices. The rational mappings describing the models' statistical properties
are obtained via the recurrence relation technique. We provide analytical
solutions for the superstable cycles of the second order for both models. A
particular attention is devoted to the period three window. Here we present an
exact result for the third order superstable orbit for the QSP and a numerical
solution for the TSAI model. Additionally, we point out a non-trivial
connection between bifurcations and superstability: in some regions of
parameters a superstable cycle is not followed by a doubling bifurcation.
Furthermore, we use symbolic dynamics to understand the changes taking place at
points of superstability and to distinguish areas between two consecutive
superstable orbits.Comment: 12 pages, 5 figures. Updated version for publicatio
On a type of exponential functional equation and its superstability in the sense of Ger
In this paper, we deal with a type exponential functional equation as follows
where and are two real valued functions on a
commutative semigroup. Our aim of this paper is to proved that the above
functional equation in the sense of Ger is superstable
- …