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The Role of Adaptation in Plankton System with Beddington-DeAngelis Type Functional Response

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Mathematical Modelling and Scientific Computing with Applications (ICMMSC 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 308))

Abstract

In this paper two interacting species in presence of adaptation (dormancy of the predators such as resting eggs) has been discussed. The dormant stage is an equipment to survive in harsh environment. We have discussed the stability analysis of system without diffusion and in presence of diffusion. Our numerical investigation reveals that above the critical value of interference among the zooplankton the system become stable. Spatiotemporal pattern shows a transient complex spatiotemporal pattern by increasing the time and space.

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References

  1. Harper, J.L.: Population Biology of Plants. Academic Press, London (1977)

    Google Scholar 

  2. Wiggins, G.B., Mackay, R.J., Smith, I.M.: Evolutionary and ecological strategies of animals in annual temporary pools. Arch. Hydrobiol. Suppl. 58, 97–206 (1980)

    Google Scholar 

  3. Henis, Y.: Survival and Dormancy of Microorganisms. Wiley, Hoboken (1987)

    Google Scholar 

  4. Piltz, S.H., Porter, M.A., Maini, P.K.: Prey switching with a linear performance trade-off. SIAM J. Appl. Dyn. Syst. 13, 658–682 (2014)

    Article  MathSciNet  Google Scholar 

  5. De Stasio Jr., B.T.: The role of dormancy and emergence patterns in the dynamics of a freshwater zooplankton community. Limnol. Oceanogr. 35, 1079–1090 (1990)

    Article  Google Scholar 

  6. Hutchinson, G.E.: A Treatise on Limnology. Wiley, Hoboken (1967)

    Google Scholar 

  7. Slusarczyk, M.: Food threshold for diapause in Daphnia under the threat of fish predation. Ecology 82, 1089–1096 (2001)

    Article  Google Scholar 

  8. Slusarczyk, M.: Predator-induced diapauses in Daphnia. Ecology 76, 1008–1013 (1995)

    Article  Google Scholar 

  9. De Stasio, B.T.: The role of dormancy and emergence patterns in the dynamics of a freshwater zooplankton community. Limnol. Oceanogr. 35, 1079–1090 (1990)

    Article  Google Scholar 

  10. Kuwamura, M., Nakazawa, T., Ogawa, T.: A minimum model of prey-predator system with dormancy of predators and the paradox of enrichment. J. Math. Biol. 58, 459–479 (2009)

    Article  MathSciNet  Google Scholar 

  11. Kuwamura, M., Chiba, H.: Mixed-mode oscillations and chaos in a prey-predator system with dormancy of predators. Chaos 19, 043121 (2009)

    Article  MathSciNet  Google Scholar 

  12. Nakazawa, T., Kuwamura, M., Yamamura, N.: Implications of resting eggs of zooplankton for the paradox of enrichment. Popul. Ecol. 53, 341–350 (2011)

    Article  Google Scholar 

  13. Wang, J., Jiang, W.: Bifurcation and chaos of a delayed predator-prey model with dormancy of predators. Nonlinear Dyn. 69, 1541–1558 (2012)

    Article  MathSciNet  Google Scholar 

  14. Kuwamura, M.: Turing instabilities in prey-predator systems with dormancy of predators. J. Math. Biol. 71, 125–149 (2015)

    Article  MathSciNet  Google Scholar 

  15. Upadhyay, R.K., Thakur, N.K., Rai, V.: Diffusion driven instabilities and spatio-temporal patterns in an aquatic predator-prey system with Beddington-DeAngelis type functional response. Int. J. Bifur. Chaos 21, 663–684 (2011)

    Article  MathSciNet  Google Scholar 

  16. Scheffer, M.: Ecology of Shallow Lakes. Chapman and Hall, London (1998)

    Google Scholar 

  17. Garvie, M.R.: Finite difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB. Bull. Math. Biol. 69, 931–956 (2007)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This research work is supported by Chhattisgarh Council of Science and Technology, India under grant no. 2238/CCOST/MRP/2015 to the corresponding author (Nilesh Kumar Thakur).

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Correspondence to Nilesh Kumar Thakur .

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Thakur, N.K., Ojha, A., Tiwari, S.K. (2020). The Role of Adaptation in Plankton System with Beddington-DeAngelis Type Functional Response. In: Manna, S., Datta, B., Ahmad, S. (eds) Mathematical Modelling and Scientific Computing with Applications. ICMMSC 2018. Springer Proceedings in Mathematics & Statistics, vol 308. Springer, Singapore. https://doi.org/10.1007/978-981-15-1338-1_2

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