Linear stability and dynamics of a periodic directional chain of fractional relaxors in an anharmonic potential

Abstract

We derive linear stability conditions for a periodic directional chain of an odd number of fractional relaxors in an anharmonic potential. The Hopf bifurcation point of this system and the oscillation characteristics of the resulting limit cycles are established in terms of the potential, fractional order, and coupling parameters. We also obtain time series solutions to the equations of motion of these relaxors by a modified Adams-Bashforth-Moulton predictor-corrector algorithm. These simulations give qualitative insight into the changes in the dynamics of our system when the system parameters are continuously varied.