Stability for stochastic nonlinear dynamical systems and applications

• Grant number: 21/12213-5
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: July 01, 2022
• End date: June 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Márcia Cristina Anderson Braz Federson
• Grantee: Fernanda Andrade da Silva
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 20/14075-6 - Dynamical systems and their attractors under perturbations, AP.TEM
• Associated scholarship(s): 23/09056-0 - Stability for stochastic partial differential equations in the framework of Kurzweil-belated integral, BE.EP.PD

Abstract

This project aims to investigate the existence and uniqueness of a solution for a retarded stochastic differential equation defined on a Banach space whose integral form is in the sense of Itô-Kurzweil-Henstock. We intend to relate the concept of stability in probability for this equation to the existence of a Lyapunov functional. We are also interested in applying the results to Quantum Mechanics, to the stabilization control problem of the inverted pendulum and to a mathematical model of the spread of infectious diseases.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SILVA, F. ANDRADE DA; BONOTTO, E. M.; FEDERSON, M.. Stability for generalized stochastic equations. Stochastic Processes and their Applications, v. 173, p. 14-pg., 2024-04-20. (21/12213-5)