https://doi.org/10.1140/epjp/s13360-025-06078-6
Regular Article
Lagrangians and Newtonian analogs for biological systems
1
Institute of Systems Science, Durban University of Technology, 4000, Durban, South Africa
2
Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta, Chile
3
School of Technology, Woxsen University, 502345, Hyderabad, Telangana, India
4
National Institute for Theoretical and Computational Sciences, NITheCS, Durban, South Africa
5
Department Institute for Water and Wastewater Technology (IWWT), Durban University of Technology, 4000, Durban, South Africa
Received:
11
November
2024
Accepted:
1
February
2025
Published online:
4
March
2025
This study investigates the potential for biological systems to be governed by a variational principle, suggesting that such systems may evolve to minimize or optimize specific quantities. To explore this idea, we focus on identifying Lagrange functions that can effectively model the dynamics of selected population systems. These functions provide a deeper understanding of population evolution by framing their behavior in terms of energy-like variables. We present an algorithm for generating Lagrangian functions applicable to a family of population dynamics models and demonstrate the equivalence between two-dimensional population models and a one-dimensional Newtonian mechanical analog. Furthermore, we explore the existence of conservation laws for these models, utilizing Noether’s theorems to investigate their implications.
© The Author(s) 2025
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