Bifurcations in a Mathematical Model for Study of the Human Population and Natural Resource Exploitation

In Colombia, there are reports of regions which have reached minimum natural resource thresholds. Among of the main causes thereof is the absence of institutional control actions. This absence is reflected in high rates of deforestation, water pollution, famine, and poverty, to name a few. For example, in La Guajira, a region where emeralds, coal, and petroleum are extracted, these activities have generated water pollution, which diminishes fishing activity, and which causes landslides, and the eviction and displacement of communities, who leave their land and agriculture practices behind (CINEP Programa por la paz, Informe especial: Minería, conflictos agrarios y ambientales en el sur de la Guajira (in Spanish) (2016), http://www.cinep.org.co/imagesinstitucionalinformes_especialesInforme_Especial-Mineria_La_Guajira.pdf ). El Departamento Administrativo de Estadstica (DANE) revealed that, for 2014, said region exhibited a reduction in agricultural production, livestock farming, hunting, forestry, and fishing, of up to −5.2%, and little mining or quarrying growth (a scant 1.5%) (ICER, Informe de conyuntura económica regional. Departamento de la Guajira (in Spanish) (2015), https://www.dane.gov.co/files/icer/2015/ICER_La_Guajira2015.pdf ). In this investigation, a mathematical model is presented, which makes the study of the dynamics of the following variables possible: human population, forest stock, fish stock, available water, and the human features necessary to achieve equilibrium values between socioeconomic and environmental issues. A bifurcation analysis is presented for different system parameters, i.e. technology and the percentage of the population dedicated to each economic sector. Special attention was paid to water consumption, energy production, and food production, owing to their everyday consumption relevance and necessitude. “If the human population increases, its consumption will also increase” (Garcia and You, Comput Chem Eng 91:49–67, 2016).