Linear dynamical systems with stochastic linear part

• Grant number: 24/23739-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2025
• End date: May 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Benito Frazao Pires
• Grantee: Ricardo Victório Cury
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

In this project, we investigate the behavior of discrete linear dynamic systems with a stochastic linear part. More precisely, consider a stochastic matrix (linear part) A of order nxn and a vector (initial state) x0 ¿ Rn+. The state x(k) of the system at time k is given recursively by the difference equation: x(k) = Ax(k ¿ 1), k > 1, where x(0) = x0. The entries of the matrix A are associated with a graph. The goal of this project is to understand under what conditions on the matrix and/or the topology of the graph, the limit limk¿¿ x(k) exists for every non-negative vector x(0). Applications of the results will also be explored to understand the dynamics of influence networks.