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Calculation of the Lyapunov exponent and the morphological period of time series in nickel oscillatory dissolution

Grant number: 19/03273-4
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): May 01, 2019
Effective date (End): April 30, 2021
Field of knowledge:Physical Sciences and Mathematics - Chemistry - Physical-Chemistry
Principal Investigator:Raphael Nagao de Sousa
Grantee:Caio da Silva Rodrigues
Home Institution: Instituto de Química (IQ). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:16/01817-9 - Design and control of self-organized electrochemical patterns, AP.JP

Abstract

This work involves the theoretical study of the oscillatory dynamics present during the dissolution of nickel in acid medium and will be solved through the approximation numerical integration method called the fourth-order Runge-Kutta. With the solution of the equations, time series will be analyzed by plotting one of the variables by time, specifically the potential of the double electric layer because it contains all the necessary physico-chemical information. The temporal series can have two temporal characteristics: chaos (non-periodic), that is, there is no repetition, and periodic, in which case it is possible to observe a restricted number of periods that the series contains. A two-dimensional map will be produced containing the periods, each axis being a control parameter that describes the system. In addition, the Lyapunov exponents will be used to characterize chaotic time series. These will be calculated using the method proposed by Alan Wolf "Determining Lyapunov Exponents from Time Series" in C.