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Full-Text Articles in Physical Sciences and Mathematics
Homogenization Techniques For Population Dynamics In Strongly Heterogeneous Landscapes, Brian P. Yurk, Christina A. Cobbold
Homogenization Techniques For Population Dynamics In Strongly Heterogeneous Landscapes, Brian P. Yurk, Christina A. Cobbold
Faculty Publications
An important problem in spatial ecology is to understand how population-scale patterns emerge from individual-level birth, death, and movement processes. These processes, which depend on local landscape characteristics, vary spatially and may exhibit sharp transitions through behavioural responses to habitat edges, leading to discontinuous population densities. Such systems can be modelled using reaction–diffusion equations with interface conditions that capture local behaviour at patch boundaries. In this work we develop a novel homogenization technique to approximate the large-scale dynamics of the system. We illustrate our approach, which also generalizes to multiple species, with an example of logistic growth within a periodic …