By Mimmo Iannelli, Andrea Pugliese
This ebook is an creation to mathematical biology for college students without adventure in biology, yet who've a few mathematical heritage. The paintings is targeted on inhabitants dynamics and ecology, following a convention 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 intensely renowned. those subject matters are used because the zone the place to appreciate sorts of mathematical modeling and the prospective that means of qualitative contract of modeling with info. The publication additionally incorporates a collections of difficulties designed to method extra complicated questions. This fabric has been utilized in the classes on the collage of Trento, directed at scholars of their fourth yr of reports in arithmetic. it will possibly even be used as a reference because it presents updated advancements in different parts.
Read or Download An Introduction to Mathematical Population Dynamics: Along the trail of Volterra and Lotka (UNITEXT, Volume 79) PDF
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Additional resources for An Introduction to Mathematical Population Dynamics: Along the trail of Volterra and Lotka (UNITEXT, Volume 79)
14) λ = −e−τλ . 14) shows that = 0 is unstable, in fact the solutions of the linearized equation are ω (t) = ω0 et , meaning that deviations tend to grow exponentially. As for eq. 15), in Sect. 15) have negative real part. 15) are in the left hand side of the complex plane. 15) changes with τ . From the analysis of the change in the location of roots, reported at the end of this chapter in Sect. 6 and displayed graphically in Fig. 15) cross the imaginary axis so that the equilibrium solution u∗ = 1 becomes unstable.
E. lim (N(t) − N∞ (t)) = 0. 3. Intraspeciﬁc competition Assume that the growth rate of a population depends on available resources ρ (t), according to a general law r(t) = G(ρ (t)). Assume for the moment that the total amount of resources is a ﬁxed constant C, but they can be free (hence available, denoted by ρ (t)) or used by the population, denoted by H(N(t)), where dependence on the population is shown. 42) and the resulting model will be speciﬁed when the functions G(·) and H(·) are given. 1.
13). 39) 34 1 Malthus, Verhulst and all that 2. 40) assuming both r(t) and m(t) periodic with period T. 40) and is periodic with period T. 3. e. lim (N(t) − N∞ (t)) = 0. 3. Intraspeciﬁc competition Assume that the growth rate of a population depends on available resources ρ (t), according to a general law r(t) = G(ρ (t)). Assume for the moment that the total amount of resources is a ﬁxed constant C, but they can be free (hence available, denoted by ρ (t)) or used by the population, denoted by H(N(t)), where dependence on the population is shown.