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Hopf bifurcation: a scaling analysis

Grant number: 15/23142-0
Support Opportunities:Scholarships in Brazil - Scientific Initiation
Effective date (Start): May 01, 2016
Effective date (End): December 31, 2018
Field of knowledge:Physical Sciences and Mathematics - Physics - General Physics
Principal Investigator:Edson Denis Leonel
Grantee:Vinicius Barros da Silva
Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
Associated scholarship(s):16/18975-6 - Bistable laser with long-delayed feedback: a scaling investigation, BE.EP.IC

Abstract

Phase transitions can be described by the use of scaling laws. In statistical physics, phase transitions are related to changes in the spatial structure of the system, particularly due to the variation of control parameters. On the other hand in dynamical systems, the phase transitions are linked to modifications in the structure of the phase space of the system, also due to changes in the control parameters. Indeed, near to a phase transition, the system exhibits observables that are described by a scaling function and critical exponents characterize the dynamics near the transition. In this project, we investigate some scaling properties observed in the convergence towards the fixed point in the Hopf bifurcation. We are particularly interested in describing the dynamics at the bifurcation and around it by using a scaling similar to the one used in phase transition in statistical mechanics.

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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)
DA SILVA, VINICIUS BARROS. Statistical scaling laws for chemical oscillators. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 509, p. 66-73, . (16/18975-6, 15/23142-0)
DA SILVA, VINICIUS BARROS. Statistical Scaling Laws for Competing Biological Species. COMPLEX SYSTEMS, v. 27, n. 4, p. 355-367, . (16/18975-6, 15/23142-0)

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