Chaos in Simple Rotation-Translation Models

Abstract

The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting trajectories in the plane are explored and illustrated in the computer experiments done. Characteristic patterns, egg-shaped forms and central chaotic bulges are present when particles are introduced in the rotating system. The resulting forms and chaotic attractors mainly depend on the form of the nonlinear function expressing the rotation angle. Several cases are studied corresponding to a central force rotation system.