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Plant Dynamics, Birth-Jump Processes, and Sharp Traveling Waves
Ist Teil von
Bulletin of mathematical biology, 2018-06, Vol.80 (6), p.1655-1687
Ort / Verlag
New York: Springer US
Erscheinungsjahr
2018
Link zum Volltext
Quelle
SpringerNature Journals
Beschreibungen/Notizen
Motivated by the importance of understanding the dynamics of the growth and dispersal of plants in various environments, we introduce and analyze a discrete agent-based model based on a
birth-jump process
, which exhibit wave-like solutions. To rigorously analyze these traveling wave phenomena, we derive the diffusion limit of the discrete model and prove the existence of traveling wave solutions (sharp and continuously differentiable) assuming a logarithmic-type growth. Furthermore, we provide a variational speed for the minimum speed of the waves and perform numerical experiments that confirm our results.