Characterizing Transitioning in Chaotic Models

Abstract

In order to understand how complicated physical systems behave, we study idealized systems instead and interpret the qualitative behavior. In order to understand how non-linear, chaotic systems transition into new parameter sets, we characterize the distribution of dynamical points over the manifold of trajectories (also known as the “strange attractor”) for the Lorenz model under two regimes. We consider the effects of variation of just one of the three parameters of the Lorenz model. First, we establish measures of shape of the distribution over the manifold for a range of static values of that parameter. Then, the same measures of shape are calculated for the trajectory that results when a parameter is ramped linearly in time. Statistical comparison of these distributions will be used to describe the evolution of the attractor. This simple model can illustrate how such non-linear, chaotic systems behave when the parameters of the system vary.