Analysis of attractor patterns and behavior for the laser with injected signal
Abstract
In this dissertation an understanding of the properties and characteristics of coexisting attractors is discussed. Lyapunov exponent (LE) patterns are shown to be predictors of the dynamics of the laser with injected signal (LIS). These patterns are believed to be universal and can be applied to any nonlinear system with a simple control parameter. Patterns such as steady states, limit cycles, bifurcations, torus behavior, and chaos are known to exist. The patterns are found using the full LE spectrum to also predict (i) attractor domains that are surrounded by converging and diverging LEs; (ii) bifurcation sequences with the appearance of asymmetric bubbles; and (iii) imminent bifurcation with the appearance of a symmetric-like bubble before or after a system parameter is changed. These predictors are shown to exist in an optomechanical system as well. Further, the system is evaluated using incremental perturbations of the state parameters in the LIS model. The perturbation study shows the potential for dynamical changes in the system and different attractor selection. By plotting the percent occurrences that transition to a coexisting attractor against the different values of the perturbations, the system shows distinct pattern variations and distinct differences between positive and negative perturbations. The structures are compared to the basins of attraction to analyze their effects on predicting which attractor the system lands.
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- OSU Dissertations [11222]