Period Doubling Bifurcations of Destroyed T(2) Tori

With the availability of computing power to researchers, the study of nonlinear systems has increased tremendously. Systems which were previously too calculation intensive to be studied in an efficient manner, such as systems of a large number of coupled oscillators, are now open to investigation, and thus a number of researchers have begun to examine these systems. Due to the complications in trying to analyze the microdynamics of these systems, the studies which are performed tend to be of a statistical nature. In addition to the study of systems of a large number of coupled oscillators, systems consisting of just a single oscillator have been researched extensively. However, a much more difficult problem consists of a system of just a coupled few oscillators. With just a few coupled oscillators, the population is not large enough for statistical methods, and the phase space is large enough to make these systems difficult to analyze. In order to understand the dynamics of a large set of oscillators, one needs to understand the dynamics of just a few oscillators. In this work, we look at two driven, damped Duffing oscillators with additive coupling and observe the various complex phenomena which occur in a nonlinear system and how they compete in parameter space. In particular, we explore the period doubling bifurcations of a T ^2 torus and the destruction of a T ^2 torus. Finally, we introduce a new bifurcation which occurs as we follow a path in parameter space, a period doubling bifurcation of a destroyed T^2 torus.