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Fractal Boundaries between chaos and periodicity in the parameters space.

Grant number: 13/26598-0
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Start date: June 01, 2014
End date: July 01, 2019
Field of knowledge:Physical Sciences and Mathematics - Physics - Classical Areas of Phenomenology and Applications
Principal Investigator:Iberê Luiz Caldas
Grantee:Everton Santos Medeiros
Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:18/03211-6 - Non linear dynamics, AP.TEM
Associated scholarship(s):17/05521-0 - Tipping points triggering extinctions in ecological networks, BE.EP.PD   15/20407-3 - Investigating tipping points after-effects, BE.EP.PD

Abstract

Nonlinear dynamical systems might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predicability of tunning parameters that lead these systems to either a chaotic or a periodic behavior. Here we propose to analyze such uncertainties to obtain the boundary dimension between chaos and periodicity in the parameters space. We will verify if this boundary dimension is universal for different classes of dynamical systems. Additionally, we will investigate how the size of periodic structures varies in the parameters space.

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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)
RAPHALDINI, BRENO; CIRO, DAVID; MEDEIROS, EVERTON S.; MASSAROPPE, LUCAS; TRINDADE, RICARDO I. F.. Evidence for crisis-induced intermittency during geomagnetic superchron transitions. Physical Review E, v. 101, n. 2, . (18/03211-6, 15/50686-1, 13/26598-0, 17/23417-5)
MEDEIROS, EVERTON S.; CALDAS, IBERE L.; BAPTISTA, MURILO S.; FEUDEL, ULRIKE. Trapping Phenomenon Attenuates the Consequences of Tipping Points for Limit Cycles. SCIENTIFIC REPORTS, v. 7, . (13/26598-0, 15/20407-3, 11/19296-1)
MEDEIROS, EVERTON S.; MEDRANO-T, RENE O.; CALDAS, IBERE L.; FEUDEL, ULRIKE. The impact of chaotic saddles on the synchronization of complex networks of discrete-time units. JOURNAL OF PHYSICS-COMPLEXITY, v. 2, n. 3, . (15/50122-0, 17/05521-0, 13/26598-0, 18/03211-6)
RAPHALDINI, BRENO; MEDEIROS, EVERTON S.; CIRO, DAVID; FRANCO, DANIEL RIBEIRO; TRINDADE, RICARDO I. F.. Geomagnetic reversals at the edge of regularity. PHYSICAL REVIEW RESEARCH, v. 3, n. 1, . (17/23417-5, 18/03211-6, 13/26598-0)
MEDEIROS, EVERTON S.; MEDRANO-T, RENE O.; CALDAS, IBERE L.; FEUDEL, ULRIKE. Boundaries of synchronization in oscillator networks. PHYSICAL REVIEW E, v. 98, n. 3, p. 5-pg., . (11/19296-1, 13/26598-0, 15/50122-0, 17/05521-0)
MEDEIROS, EVERTON S.; MEDRANO-T, RENE O.; CALDAS, THERE L.; TEL, TAMAS; FEUDEL, ULRIKE. State-dependent vulnerability of synchronization. PHYSICAL REVIEW E, v. 100, n. 5, p. 7-pg., . (15/50122-0, 13/26598-0, 18/03211-6, 17/05521-0)
MEDEIROS, EVERTON S.; MEDRANO-T, RENE O.; CALDAS, IBERE L.; FEUDEL, ULRIKE. Boundaries of synchronization in oscillator networks. Physical Review E, v. 98, n. 3, . (11/19296-1, 17/05521-0, 13/26598-0, 15/50122-0)
MEDEIROS, EVERTON S.; MEDRANO-T, RENE O.; CALDAS, THERE L.; TEL, TAMAS; FEUDEL, ULRIKE. State-dependent vulnerability of synchronization. Physical Review E, v. 100, n. 5, . (18/03211-6, 17/05521-0, 13/26598-0, 15/50122-0)
MEDEIROS, E. S.; CALDAS, I. L.; BAPTISTA, M. S.. Sensitive dependence on parameters of continuous-time nonlinear dynamical systems. CHAOS SOLITONS & FRACTALS, v. 99, p. 16-19, . (11/19296-1, 13/26598-0)
RAPHALDINI, BRENO; CIRO, DAVID; MEDEIROS, EVERTON S.; MASSAROPPE, LUCAS; TRINDADE, RICARDO I. F.. Evidence for crisis-induced intermittency during geomagnetic superchron transitions. PHYSICAL REVIEW E, v. 101, n. 2, p. 8-pg., . (13/26598-0, 15/50686-1, 18/03211-6, 17/23417-5)