[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Discontinuity, Nonlinearity and Complexity
ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Effect of Prey Density Dependent Predator Intraspecific Competition Rate in a Fear Induced Predator-Prey System

Discontinuity, Nonlinearity, and Complexity 15(3) (2026) 353--363 | DOI:10.5890/DNC.2026.09.005

Debasis Mukherjee

Department of Mathematics, Vivekananda College, Thakurpukur, Kolkata-700063, India

Download Full Text PDF

 

Abstract

This article proposes and analyzes a fear-induced predator-prey model incorporating prey density-dependent predator intra-specific competition. The study focuses on how non-constant predator intra-specific competition affects the dynamics of the system. The investigation explores various aspects, including positivity, boundedness, local and global stability, uniform persistence, and Hopf bifurcation. Numerical simulation supports theoretical results, offering practical insights into the model behaviour.

Acknowledgments

The author is grateful to the anonymous reviewers for their helpful comments for improving the paper.

References

  1. [1]  Cheng, Z., Lin, Y., and Cao, J. (2006), Dynamical behaviours of partial dependent predator-prey system, Chaos, Solitons and Fractals, 28, 67-75.
  2. [2]  Lindstrom, T. (1993), Qualitative analysis of a predator-prey systems with limit cycles, Journal of Mathematical Biology, 31, 541-561.
  3. [3]  Liu, B., Leng, Z., and Chen, E.L. (2006), Analysis of a predator-prey model with Holling type II concerning impulsive control strategy, Journal of Computational and Applied Mathematics, 193, 347-362.
  4. [4]  Ruan, S. and Xiao, D. (2001), Global analysis in a predator-prey system with nonmonotonic functional response, SIAM Journal of Applied Mathematics, 61, 1445-1472.
  5. [5]  Mukherjee, D. (2022), The effect of interference time in a predator-prey-nonprey system, International Journal of Modeling, Simulation, and Scientific Computing, 13, 2250022, https://doi.org/10.1142/S1793962322500222.
  6. [6]  Mukherjee, D. (2022), Fear induced dynamics on Leslie-Gower predator-prey system with Holling type IV functional response, Jambura Journal of Biomathematics, 3, 49-57.
  7. [7]  Zanette, L.Y., White, A.F., Allen, M.C., and Michael, C. (2011), Perceived predation risk reduces the number of offspring songbirds produce per year, Science, 334, 1398-1401.
  8. [8]  Wang, X., Zanette, L., and Zou, X. (2016), Modelling the fear effect in predator-prey interactions, Journal of Mathematical Biology, 73, 1179-1204.
  9. [9]  Mondal, S., Maiti, A., and Samanta, G.P. (2018), Effects of fear and additional food in a delayed predator-prey model, Biophysical Reviews and Letters, 13, 157-177.
  10. [10]  Mukherjee, D. (2020), Study of fear mechanism predator-prey system in the presence of competitor for the prey, Ecological Genetics and Genomics, 15, 100052.
  11. [11]  Pal, S., Majhi, S., Mandal, S.S., and Pal, N. (2019), Role of fear in a predator-prey model with Beddington-DeAngelis functional response, Zeitschrift für Naturforschung A, 74, 581-585.
  12. [12]  Panday, P., Pal, N., Samanta, S., and Chattopadhyay, J. (2018), Stability and bifurcation analysis of a three-species food chain model with fear, International Journal of Bifurcation and Chaos, 28(01), 1850009.
  13. [13]  Sasmal, S. and Takeuchi, Y. (2018), Dynamics of a predator-prey system with fear and group defense, Journal of Mathematical Analysis and Applications, 64, 1-14.
  14. [14]  Wang, X. and Zou, X. (2017), Modelling the fear effect in predator-prey interactions with adaptive avoidance of predators, Bulletin of Mathematical Biology, 79, 1-35.
  15. [15]  Zhang, H., Cai, Y., Fu, S., and Wang, S.W. (2019), Impact of the fear effect in a prey-predator model incorporating a prey refuge, Applied Mathematics and Computations, 356, 328-337.
  16. [16]  Mukherjee, D. (2020), Role of fear in predator-prey system with intraspecific competition, Mathematics and Computers in Simulation, 177, 263-275.
  17. [17]  Creel, S., Christianson, D., Liley, S., and Winnie, J.A. (2007), Predation risk affects reproductive physiology and demography of elk, Science, 315, 960.
  18. [18]  Maghool, F.H. and Naji, R.K. (2022), The effect of fear on the dynamics of two competing prey-one predator system involving intra-specific competition, Communications in Mathematical Biology and Neuroscience, 2022(42), 1-48.
  19. [19]  Al-Momen, S. and Naji, R.K. (2023), Effect of hunting cooperation and fear in a food chain model with intraspecific competition, Communications in Mathematical Biology and Neuroscience, 2023, 119.
  20. [20]  Krebs, C.J., Boonstra, R., and Boutin, S. (2018), Using experimentation to understand the 10-year snowshoe hare cycle in the boreal forest of North America, Journal of Animal Ecology, 87, 87-100.
  21. [21]  Birkhoff, G. and Rota, G.C. (1982), Ordinary differential equation, Ginn and Co., Boston.
  22. [22]  Lawrence, P. (1991), Differential Equations and Dynamical Systems, Springer-Verlag, New York.
  23. [23]  Qiu, Z. (2008), Dynamics of a model for virulent phase T4, Journal of Biological Systems, 16, 597-611.
  24. [24]  Liu, W.M. (1994), Criterion of Hopf bifurcation without using eigenvalues, Journal of Mathematical Analysis and Applications, 182, 250-256.
  25. [25]  Hutson, V. (1984), A theorem on average Lyapunov function, Monatshefte für Mathematik, 98, 267-275.
  26. [26]  Burton, T.A. (2005), Volterra Integral and Differential Equations, 202, Elsevier.

Copyright © 2011-2026 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates