PH567-Nonlinear-Dynamics

Abstract

This project explores the novel approach of utilizing dissipative pseudorandom dynamics for signal modulation and communication. By extending the principles of Linear Feedback Shift Registers (LFSRs) into their analog counterparts, Analog Feedback Shift Registers (AFSRs), we achieve optimal pseudorandom noise generation with nonlinear dissipative entrainment properties. These systems allow for efficient message encoding and retrieval through synchronization mechanisms that overcome the limitations of conventional pseudorandom modulation. By developing both discrete and continuous-time dynamical models, we demonstrate the practical applications of these systems in communication protocols that combine the robustness of chaotic designs with the simplicity of digital spread-spectrum techniques. Our findings are inspired by and build upon the work of Gershenfeld and Grinstein in their seminal paper on this subject [Physical Review Letters, 74(25), 1995].