Stability and Hopf bifurcation dynamics of a food chain system: plant–pest–natural enemy with dual gestation delay as a biological control strategy

2018 ◽  
Vol 4 (2) ◽  
pp. 881-889 ◽  
Author(s):  
Vijay Kumar ◽  
Joydip Dhar ◽  
Harbax Singh Bhatti
2013 ◽  
Vol 864-867 ◽  
pp. 2522-2527
Author(s):  
Xu Ying Lv ◽  
Tian Wen Yao ◽  
Ding Jiang Wang

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.


2019 ◽  
Vol 29 (13) ◽  
pp. 1950178
Author(s):  
Vijay Kumar ◽  
Joydip Dhar ◽  
Harbax Singh Bhatti

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.


2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Younghae Do ◽  
Hunki Baek ◽  
Dongseok Kim

The dynamics of an impulsively controlled three-species food chain system with the Beddington-DeAngelis functional response are investigated using the Floquet theory and a comparison method. In the system, three species are prey, mid-predator, and top-predator. Under an integrated control strategy in sense of biological and chemical controls, the condition for extinction of the prey and the mid-predator is investigated. In addition, the condition for extinction of only the mid-predator is examined. We provide numerical simulations to substantiate the theoretical results.


Author(s):  
Zizhen Zhang ◽  
Huizhong Yang

In this paper, we analyze the dynamics of a delayed food chain system with harvesting. Sufficient conditions for the local stability of the positive equilibrium and for the existence of Hopf bifurcation are obtained by analyzing the associated characteristic equation. Formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis.


2020 ◽  
Vol 12 (18) ◽  
pp. 7816
Author(s):  
Vivek Kumar ◽  
Lucky Mehra ◽  
Cindy L. McKenzie ◽  
Lance S. Osborne

The early establishment of a biocontrol agent in the production system, whether in the greenhouse, nursery, or field, is essential for the success of the biological control program, ensuring growers’ profitability. In an effort to develop a sustainable pest management solution for vegetable growers in Florida, we explored the application of a preemptive biological control strategy, “Predator-In-First” (PIF), in regulating multiple pepper pests, Bemisia tabaci Gennadius, Frankliniella occidentalis Pergande, and Polyphagotarsonemus latus Banks under greenhouse and field conditions during different growing seasons. In these studies, two bell pepper cultivars (7039 and 7141) and the phytoseiid mite Amblyseius swirskii Athias–Henriot were used as a model system. Pepper seedlings (~8 week) of each cultivar were infested with varying rates of A. swirskii (20 or 40 mites/plant or one sachet/10 plant) and allowed to settle on plant hosts for a week before planting in pots or field beds. Results showed a comparative consistent performance of the treatment with the high rate of phytoseiids (40 mites/plant) in regulating B. tabaci and F. occidentalis populations in greenhouse studies, and B. tabaci and P. latus pests under field conditions. During two fall field seasons, higher marketable yields of 12.8% and 20.1% in cultivar 7039, and 24.3% and 39.5% in cultivar 7141 were observed in the treatment with the high rate of phytoseiids compared to the untreated control, indicating yield benefits of the approach. The outcome of the study is encouraging and demonstrates that PIF can be an important tool for organic vegetable growers and a potential alternative to chemical-based conventional pest management strategies. The advantages and limitations of the PIF approach in Florida pepper production are discussed.


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