Nowadays, management and regulation of natural
resources like agriculture, fisheries, forestry and wildlife is one of the
popular topics in research. The evolution of humankind is largely dependent on
the quality of the environment and the resources it provides; but numerous
human-induced factors, and climate change may drastically alter the conditions
of human sustainability. This paper deals with effect of numerous human-induced
activities on the depletion of forestry resources and wildlife population with
habitat complexity. A nonlinear mathematical model is proposed and analyzed. In
modeling process, we assume that the growth rate of wildlife population wholly
depends on forestry biomass. It is depleted by human-induced activities. Local
stability analysis of the mathematical model along with the persistence of the
system is checked by using theory of nonlinear ordinary differential equations
and Butler-McGhee lemma. Analytical results obtained are justified numerically
through numerical simulation. Important parameters are investigated and
variation of variables with change in these parameters is determined.
References
[1]
Rawat, G.S. and Ginwal, H.S. (2009) Conservation and Management of Forest Genetic Resources in India. Forest Genetic Resources Conservation and Management: Status in Seven South and Southeast Asian Countries, 21-46.
[2]
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. https://doi.org/10.1016/j.nonrwa.2009.10.007
[3]
Agrawal, M., Fatima, T. and Freedman, H.I. (2010) Depletion of Forestry Resource Biomass Due to Industrialization Pressure: A Ratio-Dependent Mathematical Model. Journal of Biological Dynamics, 4, 381-396. https://doi.org/10.1080/17513750903326639
[4]
Agrawal, M. and Devi, S. (2012) A Resource-Dependent Competition Model: Effects of Population Pressure Augmented Industrialization. International Journal of Modeling, Simulation, and Scientific Computing, 3, Article ID: 1250003(1-22).
[5]
Chaudhary, M., Dhar, J. and Sahu, G.P. (2013) Mathematical Model of Depletion of Forestry Resource: Effect of Synthetic Based Industries. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 7, 639-643.
[6]
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.
[7]
Agarwal, M. and Pathak, R. (2015) Conservation of Forestry Biomass with the Use of Alternative Resource. Open Journal of Ecology, 5, 87-109. https://doi.org/10.4236/oje.2015.54009
[8]
Shukla, J.B., Pal, V.N., Misra, O.P., Agarwal, M. and Shukla, A. (1988) Effects of Population and Industrialization on the Degradation of Biomass and Its Regeneration by Afforestation: A Mathematical Model. Journal of Biomathematics, 3, 1-9.
[9]
Shukla, J.B., Freedman, H.I., Pal, V.N., Misra, O.P., Agrawal, M. and Shukla, A. (1989) Degradation and Subsequent Regeneration of a Forestry Resource: A Mathematical Model. Ecological Modelling, 44, 219-229. https://doi.org/10.1016/0304-3800(89)90031-8
[10]
Agrawal, M. and Pathak, R. (2015) Conservation of Forestry Biomass and Wildlife Population: A Mathematical Model. Asian Journal of Mathematics and Computer Research, 4, 1-15.
[11]
Agrawal, M. and Pathak, R. (2011) Modeling the Effect of Harvesting of the Vegetation Biomass and Grazer Population on Predator Population with Habitat Complexity. International Journal of Mathematical Archive, 2, 2119-2134.
[12]
Pathak, R., Agarwal, M., Takeuchi, Y. and Shukla, J.B. (2017) Modeling the Depletion of Forest Resources Due to Population and Industrialization and Its Effect on Survival of Wildlife Species. International Journal of Mathematical Modelling and Analysis of Complex Systems (IJMMACS): Nature and Society, 3, 37-65.
