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Bio-control of Pests in Tea: Effect of Environmental Fluctuation

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Amit Kumar Pal at Seth Anandram Jaipuria College, Kolkata
Amit Kumar Pal
  • Seth Anandram Jaipuria College, Kolkata
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Abstract and Figures

The method of bio-control of pests has been emerging as one of the prime method to control tea-pests and the pests doing damage in other plants. It has got a valiant potential to combat with the evil activities of pests. In this paper, we have taken into account the influence of uncertain environmental fluctuation by perturbing the environmental parameters by White noises characterized by Gaussian distribution with mean zero and unit spectral density. The criterion for non-equilibrium fluctuation and stability are derived. The implications of mathematical findings are discussed.
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… 
Existence of periodic solution around the interior equilibrium E∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E^*$$\end{document} for the delayed system of the deterministic version of (1) with time delay τ=0.1625>τ∗=0.1595\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau =0.1625>\tau ^*=0.1595$$\end{document} other parameter values are same as in Fig. 1
Existence of periodic solution around the interior equilibrium E∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E^*$$\end{document} for the delayed system of the deterministic version of (1) with time delay τ=0.1625>τ∗=0.1595\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau =0.1625>\tau ^*=0.1595$$\end{document} other parameter values are same as in Fig. 1
… 
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Int. J. Appl. Comput. Math (2019) 5:87
https://doi.org/10.1007/s40819-019-0666-3
ORIGINAL PAPER
Bio-control of Pests in Tea: Effect of Environmental
Fluctuation
A. K. Pal1
Published online: 30 May 2019
© Springer Nature India Private Limited 2019
Abstract
The method of bio-control of pests has been emerging as one of the prime method to con-
trol tea-pests and the pests doing damage in other plants. It has got a valiant potential to
combat with the evil activities of pests. In this paper, we have taken into account the influ-
ence of uncertain environmental fluctuation by perturbing the environmental parameters by
White noises characterized by Gaussian distribution with mean zero and unit spectral density.
The criterion for non-equilibrium fluctuation and stability are derived. The implications of
mathematical findings are discussed.
Keywords Time-delay ·Stability ·White noise ·Spectral density
Introduction
It is globally true that pests have been a major threat towards various crops and saplings.
Chemical experts have taken it as a real challenge to fixed out effective avenues to eradicate
pests. But it has often been creating problems as it getting mixed with the other components of
the atmosphere and thus creating fatal pollutants. So pests should be demolished keeping the
sanctity intact. In that case bio-control of pests which has already been discussed in previous
paper by using a tri-trophic model can be enhanced further [12].
As per the favourable climate condition tea leafs requires a warm and humid condition and
a soothing temperature between 18.33◦and 29.44◦,well distributed rain fall (1400 mm. per
annum) and drained sandy loam soil with pH 4.5–5.5. Tea soils is highly acidic and fertility
remains at a low stature. Pests in tea gardens some time appear in tandem, epidemically
in certain years. There various chemicals are executed to diminish that elaborate pest attack
violating the climate and ecological calm. Therefore the environment interest is less bothered
in order to attain large production. Various research work on this factor have revealed the
This article is part of the topical collection “Recent Advances in Mathematics and its Applications” edited by
Santanu Saha Ray.
BA. K. Pal
akpal_2002@yahoo.co.in
1Department of Mathematics, S. A. Jaipuria College, Kolkata 700005, India
123
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
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