Principles of measurement modeling in optical nonlinear dynamical systems

Abstract

The task of the paper consists in a creating the principles for measurement modeling in optical nonlinear dynamical systems (lasers, solitons, optical cryptography systems). The measurement model of such systems should contain: the input values, their time and noise dependencies, measurement uncertainties of input quantities and initial conditions, evolution function and forecasting time. It is suggested to use the measurement portrait for the case when the mathematical description of the systems is impossible. Analysis of measurement portrait allows us to calculate the fractal dimension, dynamics of the dynamic variables and the relationship of their values without knowledge of the analytical solutions of the system equations. Bifurcation points and Lyapunov exponents, the forecast time of the dynamics and other quantities can be calculated too. The principles of modeling the measurement process, proposed by the authors, provide theoretical, model and experimental studies of physical phenomena in the optical nonlinear dynamical systems, facilitate the solution of a wide range of problems with creation and management of optical systems, and study the processes of self-organization and dynamics in such systems.