Math. Model. Nat. Phenom. 13 (2018) 27 Mathematical Modelling of Natural Phenomena https://doi.org/10.1051/mmnp/2018035 www.mmnp-journal.org AN ECONOMIC-DEMOGRAPHIC DYNAMICAL SYSTEM A. Zincenko 1, * , S. Petrovskii 1 and V. Volpert 2 Abstract. Human population growth has been called the biggest issue the humanity faces in the 21st century, and although this statement is globally true, locally, many Western economies have been experiencing population decline. Europe is in fact homeland for population decline. By 2050 many large European economies are predicted to lose large parts of their population. In this work, we consider the dynamical system that corresponds to the model introduced by Volpert et al. [Nonlinear Anal. 159 (2017) 408–423]. With the help of this model, we illustrate scenarios that can lead, in the long-run, to sharp population decline and/or deterioration of the economy. We also illustrate that even when under certain conditions the population will go extinct, temporarily it might experience growth. Mathematics Subject Classification. 35Q91, 35Q92, 91D20 Received March 8, 2018. Accepted March 9, 2018. 1. Introduction Rapid human population growth has been called the biggest issue facing humanity in the 21st century [9]. It is widely believed that it may lead to resource scarcity, in particular, oil, which would inevitably lead to economic decline. Although the statement regarding population growth is globally true, OECD countries have been facing population decline. More specifically, Europe is, in fact, a homeland for a population decline. Large countries such as Ukraine, Poland, Portugal, Italy, Spain are experiencing population decline and are predicted to lose a significant part of the population by 2050. Germany, the EU economic powerhouse has been facing population decline over a generation [21], which, if unhindered can lead to catastrophic consequences such as the collapse of the pension system, economic decline, or even eventual extinction of the human population [18]. Also, according to predictions based on historical pattern, we can assume that some populations in the 21st century will experience population decline [15]. The problems associated with population decline include but are not limited to higher taxes to maintain current infrastructure. Population abundance also plays a role in peaceful exercise of power through a proportionate representation in the international organisations such as UN, European Commission, European Parliament [6]. That said, sharp population decline in the past has resulted in the change of the social structure, rise in wages. As one specific example, in 1348 a disease known as black death (probably a form of plague) came to Britain. It took lives of one third of the population in England and a similar proportion in Scotland and Wales. Following this disaster, a smaller population meant there was less need to grow cereal crops. There were labour shortages and peasants demanded higher wages. Also, a new class Keywords and phrases: Dynamical system, economic-demographic model. 1 Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK. 2 Universit´ e de Lyon, Universit´ e Lyon1, CNRS UMR 5208, Institut Camille Jordan, 69200 Villeurbanne Cedex, France. * Corresponding author: az110@le.ac.uk Article published by EDP Sciences c  EDP Sciences, 2018