Superstable cycles for antiferromagnetic Q-state Potts and three-site interaction Ising models on recursive lattices

作者：Ananikian N; Artuso R^*; Chakhmakhchyan L

来源：Communications in Nonlinear Science & Numerical Simulation, 2014, 19(10): 3671-3678.

DOI：10.1016/j.cnsns.2014.03.009

• Superstability
• Period three window
• Symbolic dynamics

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%26apos; 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 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.

• 出版日期2014-10