Bistable laser with long-delayed feedback: a scaling investigation

• Grant number: 16/18975-6
• Support Opportunities: Scholarships abroad - Research Internship - Scientific Initiation
• Start date: January 01, 2018
• End date: February 28, 2018
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Edson Denis Leonel
• Grantee: Vinicius Barros da Silva
• Supervisor: Giovanni Giacomelli
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Institution abroad: Istituto dei Sistemi Complessi (ISC), Italy
• Associated to the scholarship: 15/23142-0 - Hopf bifurcation: a scaling analysis, BP.IC

Abstract

Scaling laws are generally associated with phase transitions. In statistical physics, a phase transition is related to changes in the spatial structure of the systems, particularly due to the variation of the control parameters. However, in the study of dynamical systems phase transitions are linked to modifications of the phase space structure, also associated with the control parameter variations. Indeed, near a phase transition, the systems present some observables that are described by scale function with critical exponents, therefore, characterizing the dynamics near to the transition. In this project, we are interested in a particular kind of bifurcation that occurs when a stable spiral changes into an unstable spiral surrounded by a small but stable, nearly an elliptical limit cycle, i.e. the supercritical case of the Hopf bifurcation. Based on the scaling properties that characterize this bifurcation, our main goal is to obtain an experimental verification of the observables discussed above by considering an experimental setup characterized by a bistable system with long-delayed feedback where this type of bifurcation is made present. The experimental verification of these scaling properties, as well as the critical exponents that characterize the dynamics at and near at the supercritical case of Hopf bifurcation, will allow us to learn something new about the system's dynamics where the equations that describe the dynamics are not known precisely, it at all. In this way, an experimental scientist studying some dynamical system that exhibits a stable limit cycle can support or eliminate models based on the knowledge of these scaling properties. (AU)

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, NOV 1 2018. (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, 2018. (16/18975-6, 15/23142-0)