Reaction-diffusion modeling of the spread of spruce budworm in boreal ecosystem
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Reaction-diffusion modeling of the spread of spruce budworm in boreal ecosystem M. Humayun Kabir1,2 Received: 30 June 2020 / Revised: 14 August 2020 / Accepted: 18 August 2020 © Korean Society for Informatics and Computational Applied Mathematics 2020
Abstract Boreal forest in Canada has two main recurrent disturbances: one is fire and the other one is spruce budworm. The defoliation by spruce budworm, Choristoneura fumiferana (Clem.) (Lepidoptera: Tortricidae) was first started in British Columbia of Canada in 1957 near Liard River. Budworm outbreaks were observed in the 1960’s to 1970’s and from the mid 1980’s to the present. Spruce budworm disturbance is one of the major issues of the forest management because of the potential losses of timber and non-timber resources in the boreal forest. To develop a sustainable management of the boreal ecosystem, mathematical modeling approaches for the budworm outbreak have been progressed. For this understanding, we propose a single species reaction-diffusion model appended with Holling type II functional response. In this paper, our main goal is to understand the spreading phenomenon of spruce budworm and subsequently identify its spreading velocity. In order to determine the spreading velocity, we focus on the one-dimensional traveling wave solutions of the model. Our results suggest that the minimal speed of traveling wave solutions can exhibit the spreading velocity of the spruce budworm in boreal forests. Keywords Reaction-diffusion equations · Spruce budworm · Boreal forests · Traveling wave solutions Mathematics Subject Classification 35K57 · 92D45 · 35C07
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M. Humayun Kabir [email protected]
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Department of Mathematics, Jahangirnagar University, Dhaka 1342, Bangladesh
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Center for Mathematical Modeling and Applications (CMMA), Meiji University, Tokyo 164-8525, Japan
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M. H. Kabir
1 Introduction One-third of the world’s land surface is covered by forests that measures more than 39.63 million square kilometers. One may find all types of habitats within this huge area. Every forest has some specific characteristics, but some of them share common traits based on the local climate. Boreal forest is one of the four categories of forests all over the world. Boreal forests are full of life that’s adjusted to withstand frosty temperatures year-round, such as animals that can migrate long distances every winter. The most common deciduous trees found in the boreal forest, e.g. white birch, trembling aspen and balsam poplar, etc. The coniferous species including black & white spruce, jack pine, and tamarack found in the boreal forest. Boreal forests cover vast expanses in Canada, Alaska, and Russia. Boreal forests absorb carbon dioxide, the main contributor to global warming and climate change, removing it from the atmosphere and helping to keep the entire planet healthy [1]. The deciduous trees grow leaves in the summer to take advantage of photosynthesis and nutrient assimilation, and then shed them before the onset of winter. This prevents the tree from collect
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