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Mathematical Study of Hybrid Impulsive Pest Control Model with Stage Structuring


Affiliations
1 JC DAV College, Dasuya, Punjab, India
2 IKG PTU, Kapurthala, Punjab, India
3 Beant College of Engineering and Technology, Gurdaspur, Punjab, India
     

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It is a need of time to use hybrid approach (biological and chemical) to control agriculture pests effectively, economically and safely. Most of the pests and natural enemies in their life history goes through two stages namely immature larva and mature adult. From this biological point of view, we purpose a pest control model with stage structuring in pests and natural enemies in the presence of impulsively released natural enemy and chemical pesticides. Using Floquet theory and small ampli- tude perturbation technique, the local stability of periodic solutions are discussed. The suffcient conditions for the global attractively of pest- extinction periodic solution and permanence of the system are obtained by using comparison technique of differential equations with impulsive effect. At last an extensive simulation is done to verify the theoretical ndings and to see the rich dynamical behavior of the system.

Keywords

Pest Management, Stage Structure, Impulsive Dierential Equations, Boundedness, Stability, Permanence.
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  • Mathematical Study of Hybrid Impulsive Pest Control Model with Stage Structuring

Abstract Views: 371  |  PDF Views: 3

Authors

Bhanu Gupta
JC DAV College, Dasuya, Punjab, India
Amit Sharma
IKG PTU, Kapurthala, Punjab, India
Sanjay K. Srivastava
Beant College of Engineering and Technology, Gurdaspur, Punjab, India

Abstract


It is a need of time to use hybrid approach (biological and chemical) to control agriculture pests effectively, economically and safely. Most of the pests and natural enemies in their life history goes through two stages namely immature larva and mature adult. From this biological point of view, we purpose a pest control model with stage structuring in pests and natural enemies in the presence of impulsively released natural enemy and chemical pesticides. Using Floquet theory and small ampli- tude perturbation technique, the local stability of periodic solutions are discussed. The suffcient conditions for the global attractively of pest- extinction periodic solution and permanence of the system are obtained by using comparison technique of differential equations with impulsive effect. At last an extensive simulation is done to verify the theoretical ndings and to see the rich dynamical behavior of the system.

Keywords


Pest Management, Stage Structure, Impulsive Dierential Equations, Boundedness, Stability, Permanence.

References