Oscillation in Pest Population and Its Management: A Mathematical Study | Zendy

Samit Bhattacharyya | Zendy; Suma Ghosh | Zendy

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Oscillation in Pest Population and Its Management: A Mathematical Study

Author(s) -

Samit Bhattacharyya,

Suma Ghosh

Publication year - 2013

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2013/653080

Subject(s) - hopf bifurcation , pontryagin's minimum principle , mathematics , predation , pest analysis , oscillation (cell signaling) , population , integrated pest management , pest control , control theory (sociology) , bifurcation , optimal control , ecology , control (management) , mathematical optimization , computer science , biology , artificial intelligence , demography , physics , nonlinear system , botany , genetics , quantum mechanics , sociology

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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