Measuring nonlinearity by means of static parameters in Bernoulli binary sequences distribution: A brief approach

Abstract

This paper analyzes Bernoulli’s binary sequences in the representation of empirical nonlinear events, analyzing the distribution of natural resources, population sizes and other variables that influence the possible outcomes of resource’s usage. Consider the event as a nonlinear system and the metrics of analysis consisting of two dependent random variables 0 and 1, with memory and probabilities in maximum finite or infinite lengths, constant and equal to 1/2 for both variables (stationary process). The expressions of the possible trajectories of metric space represented by each binary parameter remain constant in sequences that are repeated alternating the presence or absence of one of the binary variables at each iteration (symmetric or asymmetric). It was observed that the binary variables [Formula: see text] and [Formula: see text] assume on time [Formula: see text] specific behaviors (geometric variable) that can be used as management tools in discrete and continuous nonlinear systems aiming at the optimization of resource’s usage, nonlinearity analysis and probabilistic distribution of trajectories occurring about random events. In this way, the paper presents a model of detecting fixed-point attractions and its probabilistic distributions at a given population-resource dynamic. This means that coupling oscillations in the event occur when the binary variables [Formula: see text] and [Formula: see text] are limited as a function of time [Formula: see text].