NUMERICAL AND THEORETICAL INVESTIGATION OF NEURAL TWO FIELD MODEL WITH DIFFUSION

• Grant number: 25/06467-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: October 01, 2025
• End date: October 15, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Nikolai Vasilievich Chemetov
• Grantee: Nikolai Vasilievich Chemetov
• Visiting researcher: Pedro Miguel Lima
• Visiting researcher institution: Instituto Superior Técnico (IST) , Portugal
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• City of the host institution: Ribeirão Preto

Abstract

In July 2022, Prof.Pedro Lima has visited Prof. Nikolai Chemetov at the Department ofComputation and Mathematics, FFCLRP, University of São Paulo, in the frame of the project"Analytical and Numerical Investigation of the Neural Field Equation", funded by FAPESP.This visit was the start of a fruitful scientific cooperation, also envolving Prof. DanieleAvitabile, from the Free University of Amsterdam, which had as aoutput one article in aprestigious international journal and various presentations at intternational conferences . Inthis work a new version of the neural field equation was considered which takes into accountboth synaptic and dendritic processing in neural interactions. Existence and uniqueness resultswere obtained for the given problem and the regularity of solutions was investigated. based onthe success of the proposed approach, we now intend, with this new project, to extend it tonew problems, namely, a recently introduced neural activity model which envolves a system oftwo integro-differential equations describing the evolution of two interacting fields.This project includes a new visit of Prof. Pedro Lima to the Department of Computation andMathematics, FFCLRP, University of São Paulo, for the continuation of the joint research workwith Prof. Nikolai Chemetov.In addition, Prof. Pedro Lima will deliver lectures at the PPGM seminar of the Department ofComputing and Mathematics - FFCLRP, University of São Paulo, where he will present themain results of the joint research. (AU)