2015/03/03 by Neil V. Budko, Budko, Neil V., F.J. Vermolen +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35L03 #35L65 #92D25 #Applied mathematics #Biological Physics (physics.bio-ph) #Computer science #Conservation law #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #FOS: Mathematics #FOS: Physical sciences #Logistic function #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematical optimization #Mathematics #Monte Carlo method #Ode #Phase space #Physics #Population #Simple (philosophy) #Space (punctuation) #Statistical physics #Statistics #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1503.00922
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2015/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Simultaneous deterministic and weakly stochastic dynamics of multiple populations described by a large system of ODE's is considered in the phase space of population sizes and ODE's parameters. We show that many practically interesting problems can be formulated as a low-dimensional phase-space conservation law and solved either explicitly or with simple iterative methods. In particular, we consider: non-interacting populations with unbounded and logistic growth, populations with randomized and biased migration, populations competing for a resource, coexisting species, and populations with phase-space interactions. The method provides an alternative to Monte Carlo simulations and may be useful in the fast analysis of biological data and/or removal of deterministic trends.