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A model for delayed effect of toxicant on resource-biomass system

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  • Gakkhar, Sunita
  • Sahani, Saroj Kumar

Abstract

A mathematical model for delayed effect of toxicant on resource-biomass system has been proposed and analyzed. It is assumed that the environmental toxicant have delayed harmful effect on the resource-biomass of the species. The accumulated toxicant in the biomass will indirectly slow down the growth of biological species. The introduction of delay in the model has lead to instability in the system. A Hopf bifurcation analysis has been performed with respect to key parameters for non-trivial equilibrium point. Numerical simulations suggest that the system may becomes chaotic with periodic input of toxicant into the system. Further, the negative feedback may control the chaos in the system.

Suggested Citation

  • Gakkhar, Sunita & Sahani, Saroj Kumar, 2009. "A model for delayed effect of toxicant on resource-biomass system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 912-922.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:2:p:912-922
    DOI: 10.1016/j.chaos.2007.08.046
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    References listed on IDEAS

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    1. Gakkhar, Sunita & Singh, Brahampal, 2006. "Dynamics of modified Leslie–Gower-type prey–predator model with seasonally varying parameters," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1239-1255.
    2. Chen, Juhn-Horng, 2008. "Controlling chaos and chaotification in the Chen–Lee system by multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 843-852.
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    Cited by:

    1. Yang, Jin & Tang, Guangyao, 2019. "Piecewise chemostat model with control strategy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 126-142.
    2. A. Misra & Kusum Lata & J. Shukla, 2014. "Effects of population and population pressure on forest resources and their conservation: a modeling study," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 16(2), pages 361-374, April.
    3. Jana, Debaldev & Pathak, Rachana & Agarwal, Manju, 2016. "On the stability and Hopf bifurcation of a prey-generalist predator system with independent age-selective harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 252-273.
    4. Prayga Mishra & Vimlesh Singh & Rajeev Kumar Singh & Akhilesh Kumari, 2021. "Optimal Management of Forestry Biomass Affected with Toxicant," International Journal of Research and Scientific Innovation, International Journal of Research and Scientific Innovation (IJRSI), vol. 8(8), pages 181-189, August.
    5. Misra, A.K. & Lata, Kusum, 2013. "Modeling the effect of time delay on the conservation of forestry biomass," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 1-11.

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