Research Article

Mathematical Analysis of Discrete Fractional Prey-Predator Model with Fear Effect and Square Root Functional Response

Volume: 43 Number: 1 March 30, 2022
Prasun Kumar Santra *
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Mathematical Analysis of Discrete Fractional Prey-Predator Model with Fear Effect and Square Root Functional Response

Abstract

This paper investigates the dynamics of a discrete fractional prey-predator system. The prey-predator interaction is modelled using the square root functional response, which appropriately models systems in which the prey exhibits a strong herd structure, implying that the predator generally interacts with the prey along the herd's outer corridor. Some recent field experiments and studies show that predators affect prey by directly killing and inducing fear in prey, reducing prey species' reproduction rate. Considering these facts, we propose a mathematical model to study herd behaviour and fear effect in the prey-predator system. We show algebraically equilibrium points and their stability condition. Condition for Neimark-Sacker bifurcation, Flip bifurcation and Fold bifurcation are given. Phase portraits and bifurcation diagrams are portraits that depict the model's behaviour based on some hypothetical data. Numerical simulations reveal the model's rich dynamics as a result of fear and fractional order.

Keywords

Fear effect., Prey-predator, Discrete, Fractional, Bifurcation, Fear effect.

References

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  5. [5] Liu, W., Jiang, Y., Flip bifurcation and Neimark-Sacker bifurcation in a discrete predator-prey model with harvesting, International Journal of Biomathematics, 13(1) (2020) ID1950093.
  6. [6] Owolabi K.M., Dynamical behaviour of fractional-order predator-prey system of Holling-type, Discrete and Continuous Dynamical Systems - Series S, 13 (3) (2020) 823-834.
  7. [7] Nosrati K., Shafiee M., Dynamic analysis of fractional-order singular Holling type-II predator--prey system, Applied Mathematics and Computation, 313 (2017) 159-179.
  8. [8] El-Saka H.A.A., Lee S., Jang B., Dynamic analysis of fractional-order predator--prey biological economic system with Holling type II functional response, Nonlinear Dynamics, 96 (1) (2019) 407-416.
  9. [9] Bonyah E., Atangana A., Elsadany A.A., A fractional model for predator-prey with omnivore, Chaos, 29 (1) (2019).
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Details

Primary Language

English

Subjects

Ecology, Environmental Sciences, Mathematical Sciences

Journal Section

Research Article

Authors

Prasun Kumar Santra * This is me
India

Publication Date

March 30, 2022

Submission Date

May 6, 2021

Acceptance Date

February 24, 2022

Published in Issue

Year 2022 Volume: 43 Number: 1

DOI

https://doi.org/10.17776/csj.934046

IZ

https://izlik.org/JA92LG78CA

Cite

RIS / Bibtex
APA
Santra, P. K. (2022). Mathematical Analysis of Discrete Fractional Prey-Predator Model with Fear Effect and Square Root Functional Response. Cumhuriyet Science Journal, 43(1), 72-76. https://doi.org/10.17776/csj.934046
AMA
1.Santra PK. Mathematical Analysis of Discrete Fractional Prey-Predator Model with Fear Effect and Square Root Functional Response. CSJ. 2022;43(1):72-76. doi:10.17776/csj.934046
Chicago
Santra, Prasun Kumar. 2022. “Mathematical Analysis of Discrete Fractional Prey-Predator Model With Fear Effect and Square Root Functional Response”. Cumhuriyet Science Journal 43 (1): 72-76. https://doi.org/10.17776/csj.934046.
EndNote
Santra PK (March 1, 2022) Mathematical Analysis of Discrete Fractional Prey-Predator Model with Fear Effect and Square Root Functional Response. Cumhuriyet Science Journal 43 1 72–76.
IEEE
[1]P. K. Santra, “Mathematical Analysis of Discrete Fractional Prey-Predator Model with Fear Effect and Square Root Functional Response”, CSJ, vol. 43, no. 1, pp. 72–76, Mar. 2022, doi: 10.17776/csj.934046.
ISNAD
Santra, Prasun Kumar. “Mathematical Analysis of Discrete Fractional Prey-Predator Model With Fear Effect and Square Root Functional Response”. Cumhuriyet Science Journal 43/1 (March 1, 2022): 72-76. https://doi.org/10.17776/csj.934046.
JAMA
1.Santra PK. Mathematical Analysis of Discrete Fractional Prey-Predator Model with Fear Effect and Square Root Functional Response. CSJ. 2022;43:72–76.
MLA
Santra, Prasun Kumar. “Mathematical Analysis of Discrete Fractional Prey-Predator Model With Fear Effect and Square Root Functional Response”. Cumhuriyet Science Journal, vol. 43, no. 1, Mar. 2022, pp. 72-76, doi:10.17776/csj.934046.
Vancouver
1.Prasun Kumar Santra. Mathematical Analysis of Discrete Fractional Prey-Predator Model with Fear Effect and Square Root Functional Response. CSJ. 2022 Mar. 1;43(1):72-6. doi:10.17776/csj.934046

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