Oscillation in Pest Population and Its Management: A Mathematical Study. (11th February 2013)

• Record Type: Journal Article
• Authors: Bhattacharyya, Samit; Ghosh, Suma
• Other Names: Srivástava H. Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2013(2013)
• Publication Date: 2013-02-11
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2013/653080
• Languages: English
• ISSNs: 0161-1712

Abstract

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.