LOCAL STABILITY ANALYSIS OF A PREDATOR-PREY DYNAMICS INCORPORATING BOTH SPECIES DENSITY INCREASING FUNCTIONAL RESPONSE

Authors:

Shilpa Samaddar,Mausumi Dhar,Paritosh Bhattacharya,

DOI NO:

https://doi.org/10.26782/jmcms.2022.01.00006

Keywords:

Predator cooperation,Prey predator system,Equilibrium points,Local stability behaviour,

Abstract

Most of the functional responses which have been incorporated to formulate mathematical biology consider individual contact or predator cooperation. In this study, we have introduced a different functional response that describes the prey-predator system when predators form a line and cooperatively attack a group of predators. We have also described the effect of prey on this system. Additionally, we find all the equilibrium points and their local stability behaviour.

Refference:

I. C. Cosner, D. L. DeAngelis, J. S. Ault, D. B. Olson, Effects of spatial grouping on the functional response of predators, Theoretical population biology 56 (1) (1999) 65–75.
II. C. S. Holling, Some characteristics of simple types of predation and parasitism1, The Canadian Entomologist 91 (7) (1959) 385–398.
III. C. S. Holling, The functional response of predators to prey density and its role in mimicry and population regulation, The Memoirs of the Entomological Society of Canada 97 (S45) (1965) 5–60.
IV. D. L. DeAngelis, R. Goldstein, R. V. O’Neill, A model for tropic interaction, Ecology 56 (4) (1975) 881–892.
V. D. Xiao, S. Ruan, Codimension two bifurcations in a predator–prey system with group defense, International Journal of Bifurcation and Chaos 11 (08) (2001) 2123–2131.
VI. H. I. Freedman, G. S. Wolkowicz, Predator-prey systems with group defence: the paradox of enrichment revisited, Bulletin of Mathematical Biology 48 (5-6) (1986) 493–508.
VII. J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, The Journal of Animal Ecology (1975) 331–340.
VIII. K.-S. Cheng, S.-B. Hsu, S.-S. Lin, Some results on global stability of a predator-prey system, Journal of Mathematical Biology 12 (1) (1982) 115–126.
IX. R. Arditi, L. R. Ginzburg, H. R. Akcakaya, Variation in plankton densities among lakes: a case for ratio-dependent predation models, The American Naturalist 138 (5) (1991) 1287–1296.

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