The Mathematical Biomodelling and Artificial Intelligence Group (GBM-IA) emerges from an already well-established body of scientific work, built upon international collaboration, advanced theoretical development, and interdisciplinary applications to complex real-world systems.

Thanks to the Research Stay Grant from the Universidad Católica de Temuco, Dr. William Campillay Llanos conducted a research visit at the Instituto de Matemática Pura e Aplicada, one of the most prestigious centers of excellence in mathematical research worldwide. This experience strengthened connections with a high-level scientific community characterized by its global impact and its focus on frontier problems.

During this stay, meaningful interactions were established with international researchers, including Honduran mathematician Juan Ramón Madrid Padilla, a collaborator of the renowned mathematician Terence Tao, reflecting the strength of the academic networks developed.

As part of the 35th Brazilian Mathematics Colloquium, advances in biomathematical modelling were presented in the thematic session Modelagem em Biomatemática sob Novos Olhares e Perspectivas. This participation opened new opportunities for collaboration with researchers from Brazil, Portugal, and other regions, including the PPGMAT-UFABC and the University of Lisbon.

Furthermore, participation in the specialized course Theory of Hyperbolic Conservation Laws, taught by Dr. Wanderson J. Lambert and Dr. Marlon López-Flores under the direction of Dr. Dan Marchesin, provided exposure to highly complex mathematical problems, highlighting the importance of perseverance and collaborative research.

This trajectory is consolidated through the creation of the GBM-IA, a binational scientific initiative that integrates differential equations, complex systems, biomodelling, and artificial intelligence, connecting advanced mathematical theory with real-world applications.

👥 Team

The group is organized under a binational co-directorship model, strengthening collaboration between Chile and Honduras:

• Dr. William Campillay Llanos (Chile) – Co-Director

• Dr. Marlon López-Flores (Honduras/Brazil) – Co-Director

The team is composed of graduate-level researchers in training:

🇭🇳 Honduras – National Autonomous University of Honduras

Students from the Master’s Program in Mathematics at the National Autonomous University of Honduras:

• Gustavo Ariel Maldonado Batres

• José David Zúniga Varela

• Carlos Miguel Cruz Rodas

🇨🇱 Chile – Universidad Católica de Temuco

Master’s students engaged in research lines related to biomodelling, artificial intelligence, and complex systems.

🔬 Research Lines

The GBM-IA is structured under a symmetric and complementary binational framework, integrating advanced theoretical development with interdisciplinary applications.

🇭🇳 Honduras – Advanced Mathematics and Theoretical Foundations

Proportional Calculus and New Mathematical Structures

This research line focuses on the development of advanced theoretical frameworks in non-classical calculus, with emphasis on proportional calculus and multiplicative approaches. New formulations of differential equations and dynamical systems are explored within non-Newtonian contexts.

The objective is to develop innovative mathematical tools that extend classical analysis and provide new perspectives for modelling complex systems.

🇨🇱 Chile – Universidad Católica de Temuco (UCT)

Crop Phenology and Climate Change

This research line focuses on the development of mathematical models to describe and predict crop phenological dynamics under climate change scenarios. Climatic variables, digital monitoring, and data analysis techniques are integrated.

The objective is to support decision-making in agricultural systems through predictive tools.

Mutualistic Dynamics in Agroecological Systems

This research line addresses ecological interactions, particularly between pollinators and fruit crops, from a mathematical modelling perspective. The effect of body size on pollination efficiency, population dynamics, and system stability is analyzed.

The objective is to understand the relationship between biodiversity and agricultural productivity through a mathematical framework.

⚖️ Integrated Approach

The GBM-IA integrates:

• Advanced theoretical development in mathematics (Honduras)

• Applications in biological and agricultural systems (Chile – UCT)

This approach creates an interdisciplinary framework connecting theory, data, and real-world systems.

🎯 Academic Strategy

The group is oriented toward the development of high-impact scientific outputs:

• Presentations at international conferences

• Publications in scientific journals

• Conference papers, including submissions to Journal of Natural Resources and Farming

• Development and completion of Master’s theses

The goal is for each student to achieve, prior to thesis defense:

• One international presentation

• One conference paper

• One completed thesis

🚀 Academic Projection

The GBM-IA is projected as a research nucleus with impact in:

• WoS/Scopus publications

• Advanced human capital formation

• International research networks

• Knowledge transfer

As a long-term strategic goal, the group envisions the creation of a:

PhD Program in Artificial Intelligence based on Mathematical Modelling

At the Universidad Católica de Temuco, aimed at training researchers capable of addressing complex problems through:

• Differential equations

• Dynamical systems

• Artificial intelligence

• Data analysis

🌍 Vision

The GBM-IA seeks to position mathematics as a central tool for understanding and transforming complex systems, integrating theory, computation, and data to address challenges in biology, agriculture, and applied sciences.