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Abstract and Applied Analysis
Volume 2013, Article ID 736058, 7 pages
http://dx.doi.org/10.1155/2013/736058
Research Article

Qualitative Analysis of a Retarded Mathematical Framework with Applications to Living Systems

1Dipartimento di Scienze Matematiche, Politecnico, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2Department of Law and Economics, University Mediterranea of Reggio Calabria and CRIOS, University Bocconi of Milan, Via dei Bianchi 2, 89127 Reggio Calabria, Italy
3Department of Management, Polytechnic University of Marche, 60121 Ancona, Italy

Received 3 September 2013; Accepted 12 November 2013

Academic Editor: Constantin Udriste

Copyright © 2013 Carlo Bianca et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper deals with the derivation and the mathematical analysis of an autonomous and nonlinear ordinary differential-based framework. Specifically, the mathematical framework consists of a system of two ordinary differential equations: a logistic equation with a time lag and an equation for the carrying capacity that is assumed here to be time dependent. The qualitative analysis refers to the stability analysis of the coexistence equilibrium and to the derivation of sufficient conditions for the existence of Hopf bifurcations. The results are of great interest in living systems, including biological and economic systems.