Open AccessStability Analysis of Integrated Pest Management with Impulsive Biological Control
Author(s) -
B. D. Gupta,
Amit Sharma,
S. K. Srivastava
Publication year - 2018
Publication title -
mathematical journal of interdisciplinary sciences
Language(s) - English
Resource type - Journals
eISSN - 2278-957X
pISSN - 2278-9561
DOI - 10.15415/mjis.2018.62007
Subject(s) - floquet theory , pest control , pest analysis , integrated pest management , mathematics , stability (learning theory) , control theory (sociology) , extinction (optical mineralogy) , natural enemies , stability theory , ecology , biology , computer science , control (management) , physics , artificial intelligence , nonlinear system , botany , paleontology , quantum mechanics , machine learning
The aim of the present work is to study the dynamics of stage-structured pest control model including biological control, i.e. by releasing of natural enemies and infected pests periodically. It is assumed that only immature susceptible pests are attacked by natural enemies admitting Beddington DeAngelis functional response and mature susceptible pests are contacted by infected pests with bilinear incidence rate and become exposed. The sufficient condition for local stability of pest extinction periodic solution is derived by making use of Floquet’s theory and small amplitude perturbation technique. The global attractivity of pest extinction periodic solution is also established by applying comparison principle of impulsive differential equations.