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.
This research output has an Altmetric Attention Score of 2. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 07 July 2018.
All research outputs
#15,012,809
of 23,094,276 outputs
Outputs from Bulletin of Mathematical Biology
#683
of 1,105 outputs
Outputs of similar age
#196,762
of 326,092 outputs
Outputs of similar age from Bulletin of Mathematical Biology
#18
of 31 outputs
Altmetric has tracked 23,094,276 research outputs across all sources so far. This one is in the 32nd percentile – i.e., 32% of other outputs scored the same or lower than it.
So far Altmetric has tracked 1,105 research outputs from this source. They receive a mean Attention Score of 4.7. This one is in the 34th percentile – i.e., 34% of its peers scored the same or lower than it.
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We're also able to compare this research output to 31 others from the same source and published within six weeks on either side of this one. This one is in the 35th percentile – i.e., 35% of its contemporaries scored the same or lower than it.
