Natural Hazards

, Volume 23, Issue 1, pp 49–64 | Cite as

Management and Maintenance of Forestry:A Catastrophic Stochastic Analysis

  • M. A. Shah
  • Usha Sharma


In this paper, we have carried out a detailedstochastic analysis of the Ludwig-Jones–Holling modelpertaining to the occasional population burst ofthe spruce budworms in the coniferous forests of Canada.Our analysis explains the abrupt burst of the populationin the form of cusp catastrophe. A qualitative recipe hasbeen suggested for avoiding the catastrophe.

Catastrophe diffusion approximation Fokker–Planck equation critical slowing down anomalous variance 


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  1. Arnold, L.: 1974, Stochastic Differential Equations, John Wiley & Sons, New York.Google Scholar
  2. Baksha, M. W.: 1997, Biology, ecology and control of Gamar defoliation, Calopepla leavana Latr. (Chrysomelidia: Coleoptera) in Bangladesh, J. Forest Science 26(2), 31–36.Google Scholar
  3. Bhat, U. N.: 1984, Elements of Applied Stochastic Processes, 2nd edn, John Wiley & Sons, New York.Google Scholar
  4. Browne, P. G.: 1968, Pest and Diseases of Forest Plantation Trees, Clarendon Press, Oxford.Google Scholar
  5. Cox, D. R. and Miller, H. D.: 1965, The Theory of Stochastic Process, Chapman and Hall, London.Google Scholar
  6. Dekker, H.: 1979, On the critical point of a Malthus-Verlhust process, J. Chem. Phys. 21, 189–191.Google Scholar
  7. Gilmore, R.: 1981, Catastrophe Theory for Scientists and Engineers, John Wiley & Sons, New York.Google Scholar
  8. Haken, H.: 1983, Synergetics, 3rd edn, Springer-Verlag, Berlin.Google Scholar
  9. Holling, C. S. (ed.): 1978, Adaptive Environment Assessment and Management, IIASA Series, Wiley, New York.Google Scholar
  10. Karmeshu, Sharma, C. L. and Jain, V. P.: 1992, Nonlinear stochastic models of innovation diffusion with multiple adoption levels, J. Sci. Ind. Res. 51, 229–241.Google Scholar
  11. Ludwig, D., Jones, D. D., and Holling, C. S.: 1978, Qualitative analysis of insect outbreak systems: The spruce budworm and forest, J. Animal Ecology 47, 315-332.Google Scholar
  12. Mathur, R. N. and Singh, B.: 1961, A list of insect pests of forest plant in India and the adjacent countries, Indian Forest Bulletin (New Series) Entomology 171(8), 60–61Google Scholar
  13. Nicolis, G. and Prigogine, I.: 1977, Self Organization in Non-Equilibrium Systems, John Wiley & Sons, New York.Google Scholar
  14. Sharma, C. L and Pathria, R. K.: Critical behaviour of a class of non-linear stochastic model with cubic interaction, Phys. Rev. A-28, 2993-3002.Google Scholar
  15. Van Kampen, N. G.: 1981, Stochastic Processes in Physics and Chemistry, North Holland, Amsterdam.Google Scholar
  16. Wright, D. J.: 1983, Catastrophe theory in management forecasting and decision making', J. Opl. Res. Soc. 34(10), 935-942.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • M. A. Shah
    • 1
  • Usha Sharma
    • 2
  1. 1.Department of StatisticsUniversity of RajshahiRajshahiBangladesh
  2. 2.Department of Statistics and Operational ResearchKurukshetra UniversityKurukshetraIndia

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