Topological methods and rigorous numerics for bifurcations of dynamical systems

• Grant number: 10/00875-9
• Support Opportunities: Regular Research Grants
• Start date: August 01, 2010
• End date: July 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcio Fuzeto Gameiro
• Grantee: Marcio Fuzeto Gameiro
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This research project consists in using rigorous numerics combined with topological methods, such as the Conley Index, to study dynamical systems and bifurcations. (AU)

Scientific publications

(12)

(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)

FIGUERAS, JORDI-LLUIS; GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE; DE LA LLAVE, RAFAEL. A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 16, n. 2, p. 1070-1088, 2017. (16/08704-5, 13/50382-7, 10/00875-9, 13/07460-7)

GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE; RICAUD, YANN. Rigorous numerics for piecewise-smooth systems: A functional analytic approach based on Chebyshev series. Journal of Computational and Applied Mathematics, v. 292, p. 654-673, JAN 15 2016. (13/50382-7, 10/00875-9, 13/07460-7)

RODRIGUES, HILDEBRANDO M.; WU, JIANHONG; GAMEIRO, MARCIO. ROBUST SYNCHRONIZATION OF PARAMETRIZED NONAUTONOMOUS DISCRETE SYSTEMS WITH APPLICATIONS TO COMMUNICATION SYSTEMS. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, v. 1, n. 4, p. 537-547, 2011. (10/00875-9)

GAMEIRO, MARCIO; HIRAOKA, YASUAKI; IZUMI, SHUNSUKE; KRAMAR, MIROSLAV; MISCHAIKOW, KONSTANTIN; NANDA, VIDIT. A topological measurement of protein compressibility. JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, v. 32, n. 1, p. 1-17, MAR 2015. (10/00875-9, 13/07460-7)

MIYAJI, TOMOYUKI; PILARCZYK, PAWEL; GAMEIRO, MARCIO; KOKUBU, HIROSHI; MISCHAIKOW, KONSTANTIN. A study of rigorous ODE integrators for multi-scale set-oriented computations. APPLIED NUMERICAL MATHEMATICS, v. 107, p. 34-47, SEP 2016. (10/00875-9, 13/07460-7)

RODRIGUES, HILDEBRANDO M.; WU, JIANHONG; GAMEIRO, MARCIO. SWITCHING SYNCHRONIZED CHAOTIC SYSTEMS APPLIED TO SECURE COMMUNICATION. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, v. 8, n. 2, p. 413-426, APR 2018. (13/07460-7, 16/08704-5, 16/21032-6, 10/00875-9, 14/12277-0)

GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE. A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto-Sivashinsky PDE. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 16, n. 1, p. 687-728, 2017. (10/00875-9, 13/50382-7, 16/08704-5, 13/07460-7)

GAMEIRO, MARCIO; HIRAOKA, YASUAKI; OBAYASHI, IPPEI. Continuation of point clouds via persistence diagrams. PHYSICA D-NONLINEAR PHENOMENA, v. 334, p. 118-132, NOV 1 2016. (10/00875-9, 13/07460-7)

GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE; PUGLIESE, ALESSANDRO. Computation of Smooth Manifolds Via Rigorous Multi-parameter Continuation in Infinite Dimensions. FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, v. 16, n. 2, p. 531-575, APR 2016. (10/00875-9, 13/07460-7)

BUSH, JUSTIN; GAMEIRO, MARCIO; HARKER, SHAUN; KOKUBU, HIROSHI; MISCHAIKOW, KONSTANTIN; OBAYASHI, IPPEI; PILARCZYK, PAWEL. Combinatorial-topological framework for the analysis of global dynamics. Chaos, v. 22, n. 4, DEC 2012. (10/00875-9)

GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE. EFFICIENT RIGOROUS NUMERICS FOR HIGHER-DIMENSIONAL PDEs VIA ONE-DIMENSIONAL ESTIMATES. SIAM JOURNAL ON NUMERICAL ANALYSIS, v. 51, n. 4, p. 2063-2087, 2013. (10/00875-9)

GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE. Existence of secondary bifurcations or isolas for PDEs. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 74, n. 12, p. 4131-4137, AUG 2011. (10/00875-9)