Stage-structured plant-pest-natural enemy interaction dynamics incorporating gestation delay for both pest and natural enemy

2018 ◽  
Vol 5 (1) ◽  
pp. 59-69 ◽  
Author(s):  
Vijay Kumar ◽  
Joydip Dhar ◽  
Harbax Singh Bhatti
Keyword(s):  
Natural Enemy ◽  
Gestation Delay ◽  
Interaction Dynamics ◽  
Plant Pest

Bifurcation in Plant-Pest-Natural Enemy Interaction Dynamics with Gestation Delay for Both Pest and Natural Enemy

2019 ◽  
Vol 29 (13) ◽  
pp. 1950178
Author(s):  
Vijay Kumar ◽  
Joydip Dhar ◽  
Harbax Singh Bhatti
Keyword(s):  
Natural Enemy ◽  
Equilibrium Points ◽  
Model Parameters ◽  
Natural Control ◽  
Control Approach ◽  
Gestation Delay ◽  
Interior Equilibrium ◽  
Interaction Dynamics ◽  
Plant Pest ◽  
Different Levels

During this analysis, as per natural control approach in pest management, a plant-pest dynamics with biological control is proposed, here assuming that the pest and natural enemy are having different levels of gestation delay and harvesting rate of pests by natural enemy follows Holling type-III response function. Boundedness and positivity of the system are studied. Equilibria and stability analysis is carried out for possible equilibrium points. The existence of Hopf bifurcation at interior equilibrium is presented. The sensitivity analysis of the system at interior equilibrium point for model parameters has been explored. Numerical simulations are performed to support our analytic findings.

The Model of the Integrated Control of Plant Pests with Natural Enemy

2013 ◽  
Vol 864-867 ◽  
pp. 2522-2527
Author(s):  
Xu Ying Lv ◽  
Tian Wen Yao ◽  
Ding Jiang Wang
Keyword(s):  
Biological Control ◽  
Natural Enemy ◽  
Integrated Control ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Plant Pests ◽  
First Approximation ◽  
Plant Pest ◽  
The Stability ◽  
Hurwitz Theorem

This paper mainly indicates the pest-control problem by using the biological control and the pesticide control. Firstly, it analyzed the continuous changing population of the three species-plants, plant pest and natural enemy-and the pesticides’ effects to establish a three-species model of the pests’ integrated control. Secondly, the pest equilibrium points with the natural enemy and that without natural enemy were obtained. We discussed the stability of the equilibrium points by the Hurwitz theorem and the first approximation method of stability and got the sufficient conditions for asymptotic stability. Finally, numerical simulations were performed by Matlab to analyze and verify the integrated control of plant pests in the situations with some natural enemies and without enemy. Moreover, the effects of spraying pesticides which have different killing rates on enemy and plant pest were analyzed.

scholarly journals Plant-Pest-natural enemy model with impulsive biological and chemical control

2018 ◽  
pp. 413-431
Author(s):  
Vandana Kumari ◽  
Sudipa Chauhan ◽  
Sumit Kaur Bhatia ◽  
Joydip Dhar
Keyword(s):  
Natural Enemy ◽  
Chemical Control ◽  
Plant Pest
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