Analysis of Special Cases in the Study of Bifurcations of Periodic Solutions of the Ikeda Equation

Abstract

One of the special cases is associated with the formation of paired equilibrium states (a stable and an unstable one). An analysis of bifurcations in this case provides an explanation of the formation of the "boiling points of trajectories", when a periodic solution arises "out of nothing" at some point in the phase space under changes of the parameters of the equation and quickly becomes chaotic.