(245i) Population Interaction Based on Occupation: Agriculturists and Industrialists

Authors: 
Verma, B., Indian Institute of Technology Madras
Pushpavanam, S., Indian Institute of Technology, Madras
Population interaction based on occupation: Agriculturists and Industrialists

Babita K.Verma and S.Pushpavanam*

 

Department of Chemical Engineering, IIT Madras, Chennai 600036, India

*Corresponding author:spush@iitm.ac.in, Tel: +91-44-22574161

There are three classical kinds of population interaction in ecological modeling: Prey-predator, competitive and mutualism [1]. These three interactions between various species results in a rich behavior in population dynamics. These interactions occur in both chemical systems and ecological systems.

Societies in the world today are moving towards being industrially developed. This has resulted in a shift in the occupation of people from agrarian to industrial. The rapid growth of economies with industrialization has raised questions on the sustainable nature of the growth. Industrial growth can have a positive as well as a negative influence on the agricultural development [2]. For instance at low levels of industrialization farming practices can become more efficient because of mechanized tools being available, while at higher levels of industrialization the land resources available for agriculture could become strained. Keeping this in mind the objective of this work is to study the population interaction in society based on their occupation. Two broad categories of occupation have been chosen i.e. agriculturists and industrialists. It is observed that this system has all the three classical kinds of interaction discussed above. An analysis of the dynamical system can help in formulation of policies by agencies to direct growth in a particular manner.

We study this model both as lumped and distributed system. A lumped model is developed by taking into account the interaction in the two populations through the products manufactured in each sector. The food that is produced by agriculturist is shared by both the population. The Industrial product in return helps to improve agricultural productivity. A two dimensional model is formulated and a linear stability analysis is performed. We also study spatiotemporal dynamics by introducing the diffusion in this model. We further investigate the type of patterns formed due to diffusion and Allee effect [3]. General conclusions are drawn from the models based on the phase portrait analysis and the physical interactions. This study helps understand the interaction between the agriculturists and industrialists and initiate policies which would result in sustainable growth.

References:

[1] J. D. Murray, Mathematical Biology I. An introduction, vol. 17. 2002.

[2] R. Tamura, â??Human capital and the switch from agriculture to industry,â? J. Econ. Dyn. Control, vol. 27, pp. 207â??242, 2002.

[3] W. Wang, Y. Cai, Y. Zhu, and Z. Guo, â??Allee-Effect-Induced Instability in a Reaction-Diffusion Predator-Prey Model,â? vol. 2013, pp. 24â??27.