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Population Dynamics

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Qualitative Theory of Volterra Difference Equations

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Abstract

This chapter is devoted to the application of Volterra difference equations in population dynamics and epidemics. We begin the chapter by introducing different types of population models including predator-prey models. Most commonly studied version of population models are described by continuous-time dynamics, whereas in real ecosystem the changes in populations of each species due to competitive interaction cannot occur continuously. Hence, discrete-time dynamical systems are often more suitable tool for modeling the dynamics in competing species. Cone theory is introduced and utilized to prove the existence of positive periodic solutions for functional difference equations. We introduce an infinite delay population model which governs the growth of population N(n) of a single species whose members compete among themselves for the limited amount of food that is available to sustain the population, and use the results on cone theory to obtain the existence of a positive periodic solution. Moreover, from a biologist’s point of view, the idea of permanence plays a central role in any competing species.

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Authors and Affiliations

  1. Department of Mathematics, University of Dayton, Dayton, OH, USA

    Youssef N. Raffoul

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  1. Youssef N. Raffoul
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Raffoul, Y.N. (2018). Population Dynamics. In: Qualitative Theory of Volterra Difference Equations. Springer, Cham. https://doi.org/10.1007/978-3-319-97190-2_5

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