A modal representation of chaotic attractors for the driven, damped pendulum chain

In this Letter we introduce a two-mode Fourier truncation of the damped driven nonlinear Schrödinger equation which captures the nature of one type of chaotic attractor for this pde. More specifically, this truncation correctly describes homoclinic crossings which are sources of temporal sensitivity along this chaotic attractor. The truncation provides a simple and explicit model dynamical system which is of interest in its own right and which can be used as a guide for analytical studies of chaotic attractors for the full pde. The most important feature of the model is that it faithfully represents the homoclinic structures of the full pde.