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International Journal of Dynamics and Control

, Volume 7, Issue 4, pp 1195–1212 | Cite as

The effect of additional food in Holling Tanner type models

  • Aladeen Basheer
  • Emmanuel Quansah
  • Rana D. ParshadEmail author
Article
  • 36 Downloads

Abstract

Biological control, the use of predators and pathogens to control target pests, is a promising alternative to chemical control. It is hypothesized that the introduced predators efficacy can be boosted by providing them with an additional food source. The current literature primarily considers models of additional food in predator–pest systems for symmetric predator functional responses—that is when the functional and numerical responses are of the same form. The purpose of the current manuscript is to show that providing predators with additional food in models where their functional response is not symmetric, such as Holling–Tanner models, is also effective in pest eradication. Results on stability, cyclicity and Turing instability in such a class of models is investigated. Our results have large scale implications for the effective design of biological control methods involving additional food.

Keywords

Additional food Stability Turing instability Biological invasions Biological control 

Mathematics Subject Classification

Primary 34C11 34D05 35K57 60H10 Secondary 92D25 92D40 

Notes

Acknowledgements

RP would like to acknowledge partial support from the National Science Foundation via DMS 1715377 and DMS 1839993.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Aladeen Basheer
    • 1
  • Emmanuel Quansah
    • 2
  • Rana D. Parshad
    • 3
    Email author
  1. 1.Mathematics DepartmentUniversity of GeorgiaAthensUSA
  2. 2.Factory Mutual InsuranceJohnstonUSA
  3. 3.Department of MathematicsIowa State UniversityAmesUSA

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