Effect of Elevated Carbon Dioxide Concentration on Plant Growth: A Mathematical Model

Shyam Sundar^1,

¹Department of Mathematics, P. S. Institute of Technology, Kanpur-209305, India

Cite this paper:
Shyam Sundar. Effect of Elevated Carbon Dioxide Concentration on Plant Growth: A Mathematical Model. American Journal of Applied Mathematics and Statistics. 2015; 3(2):59-67. doi: 10.12691/ajams-3-2-3

Abstract

The enhanced emission of carbon dioxide (CO₂) due to increased population density has significant effect on the growth of plant biomass. It is noted here that increased atmospheric carbon dioxide is absorbed by plant biomass during photosynthesis. In this paper, therefore, a nonlinear mathematical model is proposed to study the dynamics of population density dependent emission of carbon dioxide in the atmosphere. The phenomenon is assumed to be governed by three nonlinearly dependent variables namely; plant biomass density, population density and the concentration of carbon dioxide. The model is analyzed using stability theory of ordinary differential equations and numerical simulations. It is shown that the density of plant biomass increases as the concentration of carbon dioxide increases. It is, further, shown that the equilibrium density of plant biomass decreases as the density of human population increases but the concentration of carbon dioxide increases in the atmosphere. The numerical simulation confirms these analytical results.

Keywords:
mathematical model population density plant biomass density carbon dioxide (CO₂) stability

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