Scaling laws at the bifurcations

• Grant number: 15/07922-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2015
• End date: April 30, 2016
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Edson Denis Leonel
• Grantee: Gustavo Guarise Pereira
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil

Abstract

Scaling laws are commonly linked to phase transitions. In statistical mechanics, phase transitions are related to changes in the spatial structure of the system, particularly due to the variation of control parameters. In dynamical systems however, the phase transitions are linked to modification in the phase space structure, also due to the variation of the control parameters. Indeed, near a phase transition, the system has observables which are described by a scaling function with critical exponents characterizing the dynamics near such a transition. In this project we investigate the convergence toward the fixed point in a set of bifurcations observed in different systems described by differential ordinary equations in special: (I) saddle-node; (II) transcritical; and (III) pitchfork.