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Mathematical models and stabilizing bio-control mechanisms for microbial populations in a cultured environment

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  • Sree Hari Rao, V.
  • Raja Sekhara Rao, P.

Abstract

In this paper we have analyzed a limited nutrient–consumer dynamic model involving distributed time delays both in material recycling and growth response of consumer. It is established that the system exhibits instability characteristics due to the presence of time delays. Three different types of naturally feasible bio-control mechanisms are proposed. It is established that these mechanisms have a stabilizing effect on the system in their own respect. Several independent sets of sufficient conditions for the global asymptotic stability are obtained in each case. Examples and simulations are provided for a clear understanding of the results.

Suggested Citation

  • Sree Hari Rao, V. & Raja Sekhara Rao, P., 2006. "Mathematical models and stabilizing bio-control mechanisms for microbial populations in a cultured environment," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1222-1251.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:5:p:1222-1251
    DOI: 10.1016/j.chaos.2005.07.015
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    1. Hari Rao, V. Sree & Sekhara Rao, P. Raja, 2005. "Oscillations induced by the time lags in limited nutrient–consumer dynamic models," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 11-23.
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