Contributions in Mathematics and Applications III East-West J. of Mathematics, a special volume 2010, pp. 328-343 USING SINGULARITY THEORY TO ANALYSE A SPATIALLY UNIFORM MODEL OF SELF-HEATING IN COMPOST PILES T. Luangwilai ∗ , H.S. Sidhu ∗ , M.I. Nelson ∗† and X.D. Chen ‡ ∗ School of Physical Environmental and Mathematical Sciences, University of New South Wales at the Australian Defence Force Academy, Canberra, ACT 2600, Australia. e-mail: t.luangwilai@student.adfa.edu.au, h.sidhu@adfa.edu.au. † School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia. e-mail: nelsonm@member.ams.org. ‡ Department of Chemical Engineering, Monash University, Clayton, VIC 3800, Australia. e-mail: dong.chen@eng.monash.edu.au. Abstract Fires at industrial composting facilities, such as those storing indus- trial waste products like municipal solid waste (MSW) and landfills, are fairly common. In most cases these are manageable and such incidents are not destructive enough to attract attention beyond these facilities. However, over the years there have been a few notable devastating fires at such facilities. In each of these industrial processes (e.g. composting) there is an inherent increase in temperature as a consequence of the biological ac- tivity. Indeed such a temperature increase is one of the goals of the composting waste. Elevated temperatures of the order of 70 - 90 degrees Celsius have been documented within a few months (or even a few days) of forming the compost pile. Although the basic theory of spontaneous Key words: bifurcation analysis, biological heating, composting, self-heating, Semenov model, singularity theory. 2000 AMS Mathematics Subject Classification: Primary 80A20, 80A25. 328