Bulletin of Mathematical Biology

, Volume 68, Issue 6, pp 1293–1314

A Process-Based Mathematical Model on Methane Production with Emission Indices for Control

Original Article

DOI: 10.1007/s11538-006-9076-x

Cite this article as:
Chakraborty, A. & Bhattacharaya, D.K. Bull. Math. Biol. (2006) 68: 1293. doi:10.1007/s11538-006-9076-x


In this paper, a process-based mathematical model is developed for the production of methane through biodegradation. It is a three-dimensional model given by ordinary differential equations. The results of the analysis of the model are interpreted through three emission indices, which are introduced for the first time. The estimation of either one or all of them can interpret the feasibility of the equilibrium and the long-term emission tendency of methane. The vulnerability of the methane production process with respect to soil temperature effects in methanogenic phase has been discussed and a feasible condition within a specified temperature range has defined for the nonvulnerability of the methane production process and also it has shown that under the same condition, zero-emission process of methane will be nonvulnerable with respect to the soil temperature effects in methanogenic phase. Lastly, condition for zero emission of methane is also obtained and it is interpreted through the emission indices.


Stability Basin of attraction Methanogenesis Nonvulnerability Monod type-2 kinetics Liapunov function 

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  1. 1.4145 Batchelor Hall, Center for Conservation BiologyUniversity of CaliforniaRiversideUSA
  2. 2.Department of Pure MathematicsUniversity of CalcuttaKolkata 19India

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