Analytical Study of Influence of Chemical Agents in Agricultural Systems

Authors

  • M Islam Department of Mathematics, Jadavpur University, Kolkata-700032,
  • MS Uddin Mathematics Discipline, Khulna University, Khulna-9208,
  • B Islam Indian Statistical Institute, 203 B.T.Road, Kolkata -700108,
  • N Islam Dept of Mathematics, Ramakrishna Miss. Res. College Kolkata-700103
  • HP Mazumdar Physics and Applied Math Unit, Indian Statistical Institute, Kolkata -700108

DOI:

https://doi.org/10.3329/ganit.v33i0.17657

Keywords:

Prey-predator model, Permanence, Sustainability, productivity, Poincaré-Bendixson theorem, Global stability

Abstract

Modern day agriculture is dependent on the use of chemical agents for maximizing crop yield. This practice has perilous effects on the ecosystem if used in an unchecked manner. The present paper develops a mathematical model of an agricultural system that incorporates the cumulative effect of the chemical agents like pesticides, fertilizers etc. Dynamical behaviour of the system, such as boundedness, permanence and stability, are studied. Numerical simulations are carried out to study the changes in the behaviour of the system due to varying levels of potency of the chemicals. Based on these, an effort is made to determine the conditions necessary for a sustainable and productive agricultural system in presence of chemical agents. Applicability of the model in related scenarios is also discussed.

GANIT J. Bangladesh Math. Soc. Vol. 33 (2013) 41-51

DOI: http://dx.doi.org/10.3329/ganit.v33i0.17657

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Published

2014-01-13

How to Cite

Islam, M., Uddin, M., Islam, B., Islam, N., & Mazumdar, H. (2014). Analytical Study of Influence of Chemical Agents in Agricultural Systems. GANIT: Journal of Bangladesh Mathematical Society, 33, 41–51. https://doi.org/10.3329/ganit.v33i0.17657

Issue

Vol. 33 (2013)

Section

Articles

License

The copyright of GANIT: Journal of Bangladesh Mathematical Society is reserved by Bangladesh Mathematical Society (web: https://bdmathsociety.org/)