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Oscillation in Pest Population and Its Management: A Mathematical Study

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  • Samit Bhattacharyya
  • Suma Ghosh

Abstract

We study the role of predation dynamics in oscillation of pest population in insect ecology. A two-dimensional pest control model (under the use of insecticides) with time delay in predation is considered in this paper. By the Hopf bifurcation theory, we prove the existence of the stable oscillation of the system. We also consider the economic viability of the control process. First we improve the Pontryagin maximum principle (PMP) where the delay in the system is sufficiently small and control function is linear, and then we apply the improved version of PMP to perform the optimal analysis of the pest control model as a special case.

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  • Samit Bhattacharyya & Suma Ghosh, 2013. "Oscillation in Pest Population and Its Management: A Mathematical Study," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-12, February.
    • Handle: RePEc:hin:jijmms:653080
    DOI: 10.1155/2013/653080
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