Research ArticleOpen AccessGoogle Scholar indexed
Conservation of Forestry Biomass with the Use of Alternative Resource
Department of Mathematics & Astronomy, Lucknow University, Lucknow, India
Department of Mathematics & Astronomy, Lucknow University, Lucknow, India
- 1 Department of Mathematics & Astronomy, Lucknow University, Lucknow, India
- 2 Department of Mathematics & Astronomy, Lucknow University, Lucknow, India
Open Journal of Ecology·Volume 05 (2015)·Pages 87–109·Published 1 April 2015·DOI10.4236/oje.2015.54009
Copy link · social · email
Abstract
The effect of the alternative resource and time delay on conservation of forestry biomass is studied by considering a nonlinear mathematical model. In this paper, interaction between forestry biomass, industrialization pressure, toxicant pressure and technological effort is proposed and analysed. We find out the critical value of delay and observe that there is Hopf bifurcation. Using the normal form theory and the center manifold theorem, we determine the stability and direction of the bifurcating periodic solutions. Numerical simulations are given to illustrate the analytical results.
KeywordsForestry BiomassIndustrializationAlternative ResourceToxicantTechnological EffortLocal StabilityHopf Bifurcation
- Shukla, J.B., Freedman, H.I., Pal, V.N., Misra, O.P., Agarwal, M. and Shukla, A. (1989) Degradation and Subsequent Regeneration of a Forestry Resource: A Mathematical Model. Ecological Modelling, 44, 219-229. http://dx.doi.org/10.1016/0304-3800(89)90031-8
- Li, W.Z., Ju, M.T., Liu, L., Wang, Y.N. and Li, T.L. (2011) The Effects of Biomass Solid Waste Resources Technology in Economic Development. Energy Procedia, 5, 2455-2460. http://dx.doi.org/10.1016/j.egypro.2011.03.422
- Shukla, J.B., Sharma, S., Dubey, B. and Sinha, P. (2009) Modelling the Survival of a Resource Dependent Population: Effect of Toxicants (Pollutants) Emitted from the External Sources as Well as Formed by Its Precursors. Nonlinear Analysis: Real World Applications, 10, 54-70. http://dx.doi.org/10.1016/j.nonrwa.2007.08.014
- Dubey, B. and Narayanan, A.S. (2010) Modelling Effects of Industrialization, Population and Pollution on a Renewable Resource. Nonlinear Analysis: Real World Applications, 11, 2833-2848. http://dx.doi.org/10.1016/j.nonrwa.2009.10.007
- Dhar, J., Chaudhary, M. and Sahu, G.P. (2013) Mathematical Model of Depletion of Forestry Resource, Effect of Synthetic Based Industries. International Journal of Biological, Life Science and Engineering, 7, 1-5.
- Misra, A.K. and Lata, K. (2013) Modeling the Effect of Time Delay on the Conservation of Forestry Biomass. Chaos, Solitons & Fractals, 47, 1-11. http://dx.doi.org/10.1016/j.chaos.2012.10.002
- Misra, A.K., Lata, K. and Shukla, J.B. (2014) A Mathematical Model for Depletion of Forestry Resources Due to Population and Population Pressure Augmented Industrialization. International Journal of Modeling, Simulation and Scientific Computing, 5, 1-16.
- Misra, A.K., Lata, K. and Shukla, J.B. (2014) Effects of Population and Population Pressure on Forest Resources and Their Conservation: A Modeling Study. Environment, Development and Sustainability, 16, 361-374. http://dx.doi.org/10.1007/s10668-013-9481-x
- Agarwal, M. and Devi, S. (2011) A Resource-Dependent Competition Model: Effects of Toxicants Emitted from External Sources as Well as Formed by Precursors of Competing Species. Nonlinear Analysis: Real World Applications, 12, 751-766. http://dx.doi.org/10.1016/j.nonrwa.2010.08.003
- Hassard, B.D., Kzrinoff, N.D. and Wan, W.H. (1981) Theory and Application of Hopf Bifurcation: London Mathematics Society Lecture Note Series. Vol. 41, Cambridge University Press, Cambridge.