By Mimmo Iannelli, Andrea Pugliese (auth.)
This e-book is an creation to mathematical biology for college kids with out adventure in biology, yet who've a few mathematical history. The paintings is targeted on inhabitants dynamics and ecology, following a practice that is going again to Lotka and Volterra, and features a half dedicated to the unfold of infectious ailments, a box the place mathematical modeling is very renowned. those subject matters are used because the quarter the place to appreciate forms of mathematical modeling and the prospective that means of qualitative contract of modeling with info. The e-book additionally incorporates a collections of difficulties designed to method extra complex questions. This fabric has been utilized in the classes on the collage of Trento, directed at scholars of their fourth yr of experiences in arithmetic. it may even be used as a reference because it presents up to date advancements in numerous areas.
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Additional info for An Introduction to Mathematical Population Dynamics: Along the trail of Volterra and Lotka
Let us correct the equation, introducing deaths: N (t) = β N 2 (t) − μ N(t). Discuss how the dynamics changes. In particular, does the equation still have the problem of solutions going to inﬁnity in a ﬁnite time? 3. Let us introduce a limiting factor of logistic type: N (t) = β N 2 (t) − μ N(t) (1 − γ N(t)) . Show that for N0 > 0 a global solution of the problem exists. Find all non-negative equilibria and discuss their stability. 5. Generalist predation Different models arise when combining different forms of the prey growth rate with different functional responses.
Apart from extensive qualitative studies, the spruce-budworm has been the object of a detailed modeling effort, in order to identify mechanisms apt to explain the dynamics. 34) is assumed as representative of the ecosystem to provide an insight into its qualitative behavior. 34) is adopted after identifying the abundance N(t) of the budworm as the only fast variable of the ecosystem. Instead, the carrying capacity K, depending on the amount of foliage of the forest, is identiﬁed as a slow variable, hence with respect to the fast scale it can be approximated as a constant.
The Component of Predation as Revealed by a Study of Small-Mammal Predation of the European Pine Sawﬂy, The Canadian Entomologist 91, 293–320 (1959) 7. : The functional response of predators to prey density and its role in mimicry and population regulation, Memoirs of the Entomological Society of Canada 45, 5–60 (1965) 8. : Qualitative Analysis of Insect Outbreak Systems: The Spruce Budworm and Forest, Journal of Animal Ecology 47, 315–332 (1978) 9. : An Essay on the Principle of Population. J.
An Introduction to Mathematical Population Dynamics: Along the trail of Volterra and Lotka by Mimmo Iannelli, Andrea Pugliese (auth.)