Experimental Evidence for Mixed Reality States in an Interreality System, And, Generalized Resonant Forcing of Nonlinear Dynamics
This work also explores resonances of nonlinear systems. This includes time-discrete chaotic maps as well as generalized systems of nonlinear first order differential equations. The calculus of variations is used to determine the minimal additive forcing function that induces a desired terminal response. In contrast to previous efforts, in this work only select degrees of freedom are forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. Certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. The efficacy of this methodology is demonstrated with several examples.
University of Illinois - Urbana-Champaign
Networked Digital Library of Theses and Dissertations
University of Illinois at Urbana-Champaign