Evolution processes with impulses and the attractor theory

• Grant number: 14/25970-5
• Support Opportunities: Scholarships abroad - Research
• Start date: July 15, 2015
• End date: July 14, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Everaldo de Mello Bonotto
• Grantee: Everaldo de Mello Bonotto
• Host Investigator: Tomas Caraballo Garrido
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universidad de Sevilla (US), Spain

Abstract

The present project of scientific research concerns about the theory of systems which describe the evolution of process whose continuous dynamics are interrupted by abrupt changes of state. This phenomenon is called impulse. In many natural phenomena, the real deterministic models are often described by systems which involve impulses. This project lies on the investigation of qualitative properties for impulsive evolution processes. We intend to establish the theory of evolution processes with impulses and to study results about pullback attractors and pullback dissipativity for such processes. The mathematical analysis of such systems employs techniques of topological methods and dynamical system theory. (AU)

Scientific publications

(6)

(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)

BONOTTO, E. M.; COSTA FERREIRA, J.; FEDERSON, M.. UNIFORM ASYMPTOTIC STABILITY OF A DISCONTINUOUS PREDATOR-PREY MODEL UNDER CONTROL VIA NON-AUTONOMOUS SYSTEMS THEORY. DIFFERENTIAL AND INTEGRAL EQUATIONS, v. 31, n. 7-8, p. 519-546, JUL-AUG 2018. (14/25970-5, 14/21224-7)

BONOTTO, EVERALDO M.; GIMENES, LUCIENE P.; SOUTO, GINNARA M.. ASYMPTOTICALLY ALMOST PERIODIC MOTIONS IN IMPULSIVE SEMIDYNAMICAL SYSTEMS. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, v. 49, n. 1, p. 133-163, MAR 2017. (12/20933-9, 14/21224-7, 14/25970-5)

BONOTTO, EVERALDO M.; BORTOLAN, MATHEUS C.; CARABALLO, TOMAS; COLLEGARI, RODOLFO. Impulsive non-autonomous dynamical systems and impulsive cocycle attractors. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 40, n. 4, p. 1095-1113, MAR 15 2017. (14/25970-5, 14/20691-0, 13/23933-2)

BONOTTO, E. M.; BORTOLAN, M. C.; COLLEGARI, R.; CZAJA, R.. Semicontinuity of attractors for impulsive dynamical systems. Journal of Differential Equations, v. 261, n. 8, p. 4338-4367, OCT 15 2016. (14/25970-5, 14/20691-0, 13/23933-2)

BONOTTO, E. M.. Monotone impulsive dynamical systems. COLLECTANEA MATHEMATICA, v. 69, n. 1, p. 17-24, JAN 2018. (14/25970-5)

BONOTTO, E. M.; BORTOLAN, M. C.; CARABALLO, T.; COLLEGARI, R.. Attractors for impulsive non-autonomous dynamical systems and their relations. Journal of Differential Equations, v. 262, n. 6, p. 3524-3550, MAR 15 2017. (14/20691-0, 14/25970-5)