Piecewise smooth vector fields with applications in biology

• Grant number: 17/00883-0
• Support Opportunities: Regular Research Grants
• Duration: August 01, 2017 - July 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Tiago de Carvalho
• Grantee: Tiago de Carvalho
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

In this research project we will study aspects of the Ordinary Differential Equations Qualitative Theory applied to biology. Specifically speaking, we will study biological models written as piecewise smooth vector fields. Throughout this project we will analyze mathematically the structural and asymptotic stability of models for population dynamics of the predator-prey type, cancer, HIV, pest control, among others. We emphasize that the line of study proposed here is linked to issues already covered in articles published or submitted for publication by the researcher in recent years and will help the insertion of the author in the Biometry post graduation program of the UNESP-Botucatu. Thus, we expect that during the this project papers can be written and published. (AU)

Scientific publications

(10)

(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)

CRISTIANO, RONY; PAGANO, DANIEL J.; CARVALHO, TIAGO; TONON, DURVAL J.. Bifurcations at a degenerate two-fold singularity and crossing limit cycles. Journal of Differential Equations, v. 268, n. 1, p. 115-140, DEC 15 2019. (17/00883-0, 14/02134-7)

RODRIGUES, DIEGO S.; MANCERA, PAULO F. A.; CARVALHO, TIAGO; GONCALVES, LUIZ FERNANDO. Sliding mode control in a mathematical model to chemoimmunotherapy: The occurrence of typical singularities. Applied Mathematics and Computation, v. 387, DEC 15 2020. (17/00883-0, 19/10450-0)

DE CARVALHO, TIAGO; CRISTIANO, RONY; GONCALVES, LUIZ FERNANDO; TONON, DURVAL JOSE. Global analysis of the dynamics of a mathematical model to intermittent HIV treatment. NONLINEAR DYNAMICS, v. 101, n. 1, JUL 2020. (17/00883-0, 19/10450-0)

CARVALHO, TIAGO; CARDOSO, JOAO LOPES; TONON, DURVAL JOSE. Canonical Forms for Codimension One Planar Piecewise Smooth Vector Fields with Sliding Region. Journal of Dynamics and Differential Equations, v. 30, n. 4, p. 1899-1920, DEC 2018. (17/00883-0)

RODRIGUES, D. S.; MANCERA, P. F. A.; CARVALHO, T.; GONCALVES, L. F.. A mathematical model for chemoimmunotherapy of chronic lymphocytic leukemia. Applied Mathematics and Computation, v. 349, p. 118-133, MAY 15 2019. (17/00883-0)

CARVALHO, TIAGO; CRISTIANO, RONY; RODRIGUES, DIEGO S.; TONON, DURVAL J.. Global Analysis of the Dynamics of a Piecewise Linear Vector Field Model for Prostate Cancer Treatment. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, OCT 2021. (17/00883-0, 19/10450-0)

DE CARVALHO, TIAGO; FREITAS, BRUNO. BIRTH OF AN ARBITRARY NUMBER OF T-SINGULARITIES IN 3D PIECEWISE SMOOTH VECTOR FIELDS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 24, n. 9, p. 4851-4861, SEP 2019. (17/00883-0)

VICENTIN, DANIEL CHIEREGATO; MANCERA, PAULO F. A.; CARVALHO, TIAGO; GONCALVES, LUIZ FERNANDO. Mathematical model of an antiretroviral therapy to HIV via Filippov theory. Applied Mathematics and Computation, v. 387, DEC 15 2020. (17/00883-0)

CARVALHO, TIAGO; EUZEBIO, RODRIGO DONIZETE. Minimal sets and chaos in planar piecewise smooth vector fields. Electronic Journal of Qualitative Theory of Differential Equations, n. 33, p. 1-15, 2020. (17/00883-0, 19/10450-0)

CARVALHO, TIAGO; NOVAES, DOUGLAS DUARTE; GONCALVES, LUIZ FERNANDO. Sliding Shilnikov connection in Filippov-type predator-prey model. NONLINEAR DYNAMICS, v. 100, n. 3, MAY 2020. (17/00883-0, 19/10450-0, 18/16430-8, 18/13481-0, 19/10269-3)