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Analysis on Food Web Structure, Interaction, Strength and Stability of Different Mathematical Models of Prey and Predator

  • Paritosh Bhattacharya
  • Susmita Paul
  • K. S. Choudhury
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 298)

Abstract

This paper deals with the dynamics of a predator–prey model. In this paper, we put some models where the parameters of the biological growth model systematically change over time. The densities of both prey and predator populations are obtained as functions of time. We will be concerned with time intervals of the control process and time dependence of the control functions. Here we have discussed about two important growth models.

Keywords

Predator Prey Time delay Allee effect Nonlinear system 

References

  1. 1.
    Bascompte J, Melian CJ (2005) Simple trophic modules for complex food webs. Ecology 86:2868–2873CrossRefGoogle Scholar
  2. 2.
    Camacho J et al (2007) Quantitative analysis of the local structure of food webs. J Theor Biol 246:260–268CrossRefMathSciNetGoogle Scholar
  3. 3.
    Berlow EL, Brose U, Martinez ND (2008) The “Goldilocks factor” in foodwebs. Proc Natl Acad Sci USA 105:4079–4080Google Scholar
  4. 4.
    Bastolla U, Lassig M, Manrubia SC, Valleriani A (2001) Diversity patterns from ecological models at dynamical equilibrium. J Theor Biol 212:11–34CrossRefGoogle Scholar
  5. 5.
    Peterson EE, Theobald DM, VerHoef JM (2007) Geostatistical modeling on stream networks: developing valid covariance matrices based on hydrologic distance and stream flow. Freshw Biol 52:267–279CrossRefGoogle Scholar
  6. 6.
    Memmott J et al (2006) Biodiversity loss and ecological network structure. In: Pascualand M, Dunne JA (eds) Ecological networks: linking structure to dynamics in food webs. Oxford University Press, OxfordGoogle Scholar
  7. 7.
    Saez E, Gonzalez-Olivares E (1999) Dynamics on a predator–prey model. SIAM J Appl Math 59(5):1867–1878CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Freedman HI (1980) Deterministic mathematical models in population ecology. Marcel Dekker, New YorkGoogle Scholar
  9. 9.
    Ross R (1911) The prevention of malaria. Murray, LondonGoogle Scholar
  10. 10.
    Wang G, Liang X-G, Wang F-Z (1999) The competitive dynamics of populations subject to an Allee effect. Ecol Model 124:183–192CrossRefGoogle Scholar

Copyright information

© Springer India 2014

Authors and Affiliations

  • Paritosh Bhattacharya
    • 1
  • Susmita Paul
    • 1
  • K. S. Choudhury
    • 2
  1. 1.Mathematics DepartmentNIT AgartalaAgartalaIndia
  2. 2.Mathematics DepartmentJadavpur UniversityKolkataIndia

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