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Qualitative Theory of Differential Equations
Published in Vladimir A. Dobrushkin, Applied Differential Equations, 2022
One of the favorite foods of the blue whale is called krill. These tiny shrimp-like creatures are devoured in massive amounts to provide the principal food source for the huge whales. If x(t) denotes the biomass of krills and y(t) denotes the population of whales, then their interaction can be modeled by the following Lotka–Volterra equations: x˙=x0.3−0.0075y,y˙=y−0.2+0.0025x.
Introduction
Published in Vladimir A. Dobrushkin, Applied Differential Equations, 2018
(b) Find equilibrium solutions for b=0.02 and determine the type and stability of each critical point. Describe what happens to the two populations over time. (c) Answer the previous question for b=0.05. One of the favorite foods of the blue whale is called krill. These tiny shrimp-like creatures are devoured in massive amounts to provide the principal food source for the huge whales. If x(t) denotes the biomass of krills and y(t) denotes the population of whales, then their interaction can be modeled by the following Lotka-Volterra equations:x˙=x(0.3-0.0075y),y˙=y(-0.2+0.0025x).
Qualitative Theory of Differential Equations
Published in Vladimir A. Dobrushkin, Applied Differential Equations with Boundary Value Problems, 2017
9. One of the favorite foods of the blue whale is called krill. These tiny shrimp‐like creatures are devoured in massive amounts to provide the principal food source for the huge whales. If x(t) denotes the biomass of krills and y(t) denotes the population of whales, then their interaction can be modeled by the following LotkaVolterra equations: x˙=x(0.3-0.0075y),y=y(-0.2+0.0025x) $$ \dot{x} = x(0.3 - 0.0075y) , y = y( - 0.2 + 0.0025x) $$
EightyDVec: a method for protein sequence similarity analysis using physicochemical properties of amino acids
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2022
Ranjeet Kumar Rout, Saiyed Umer, Sabha Sheikh, Sanchit Sindhwani, Smitarani Pati
For an illustration of our proposed method EightyDVec, all the species of the dataset have been considered. Here, we have calculated the Euclidean distance between all the nine protein sequences as shown in Table 3. The data have been collected from the GenBank (www.ncbi.nlm.nih.gov) namely: Human (Homo sapiens, AP_000649), Gorilla (Gorilla gorilla, NP_008222), Common Chimpanzee (Pantroglodytes, NP_008196), Pygmy Chimpanzee (Pan paniscus, NP_008209), Fin Whale (Balaenopteraphysalus, NP_006899), Blue Whale (Balaenopteramusculus, NP_007066), Rat (Rattusnorvegicus, AP_004902), Mouse (Mus musculus, NP_904338), and Opossum (Didelphis virginiana, NP_007105) as shown in Table 2. From Table 3, we observed that the Euclidean distances between , , and are quite small in comparison to other species in the same family. So, these four species are more similar to each other. The distance between and is also small in that they are more similar to each other. There is also a small distance between and indicating the evolutionary closeness between them. As the Opossum species has a large distance among other species, which indicated comparatively large evolutionary between them. Corresponding to these as input, a phylogenetic tree has been constructed as shown in Figure 1. The length of the branches of the tree represents the lineages but we focused to find the close relatedness among different species. In the comparison of our approach with other ones, it has been found that there exists consistency with the result of evolution and biological history.