2023/02/28 by Giuseppe Toscani, Toscani, Giuseppe, Mattia Zanella +1 · 4 citations
Economics, Econometrics and Finance · Medicine · Social Sciences · #Adaptation and Self-Organizing Systems (nlin.AO) #Complex Systems and Time Series Analysis #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Physics and Society (physics.soc-ph) #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.2302.14573
openalex publication_date 2023/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Owing to the analogies between the problem of wealth redistribution with taxation in a multi-agent society, we introduce and discuss a kinetic model describing the statistical distributions in time of the sizes of groups of biological systems with prey-predator dynamic. While the evolution of the mean values is shown to be driven by a classical Lotka-Volterra system of differential equations, it is shown that the time evolution of the probability distributions of the size of groups of the two interacting species is heavily dependent both on a kinetic redistribution operator and the degree of randomness present in the system. Numerical experiments are given to clarify the time-behavior of the distributions of groups of the species.