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ISSN:2325-6192 (print)
ISSN:2325-6206 (online)
Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal

Email: aml@fe.up.pt

Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

Fax: +86 29 82668723 Email: jzzhang@mail.xjtu.edu.cn

Effect of Fear on Interacting Species Dynamics with Nonlinear Predator Harvesting

Journal of Environmental Accounting and Management 9(4) (2021) 403--427 | DOI:10.5890/JEAM.2021.12.006

Lakshmi Narayan Guin$^{1}$, Ayantika Mapa$^{1}$, Santabrata Chakravarty$^{2}$

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Abstract

The present pursuit concerns itself with an updated real predator-prey system based on a fear factor induced by interacting species with nonlinear predator harvesting unlike constant or linear harvesting. The diversification of system parameters gives rise to different categories of system dynamics. The system under consideration does experience bifurcation (saddle-node, transcritical and Hopf-Andronov) about the co-existence equilibrium position with respect to the choice of fear factor or nonlinear harvesting factor as a parameter of significance. The direction of the Hopf bifurcation together with the stability of the bifurcating periodic solutions are perceived through an explicit algorithm duly established by making use of the normal form and central manifold theory. The findings of the present investigation reveal that the fear factor or nonlinear harvesting factor bears the potential to influence the dynamical scenario of the interacting species remarkably.

Acknowledgments

The authors would like to communicate their sincere appreciation to the anonymous referee for helpful remarks that will help to improve the quality of the paper. The first author gratefully acknowledges the financial support in part from Special Assistance Programme (SAP-III) sponsored by the University Grants Commission (UGC), New Delhi, India (Grant No. F.$510$ / $3$ / DRS-III / $2015$ (SAP-I)).

References

  1. [1]  Bairagi, N., Chakraborty, S., and Pal, S. (2012), Heteroclinic bifurcation and multistability in a ratio-dependent predator-prey system with Michaelis-Menten type harvesting rate, Proceedings of the World Congress on Engineering, WCE 2012, London, U.K., I.
  2. [2]  Chen, J., Huang, J., Ruan, S., and Wang, J. (2013), Regulation of a prey-predator fishery by taxation: a dynamic reaction model, SIAM Journal on Applied Mathematics, SIAM, 73(5), 1876-1905.
  3. [3]  Creel, S., Christianson, Liley, D.S., and Winnie, J. A. (2007), Predation risk affects reproductive physiology and demography of elk, Science, American Association for the Advancement of Science, 315(5814), 960.
  4. [4]  Clark, C.W. and Mangel, M. (1979), Aggregation and fishery dynamics: a theoretical study of schooling and the purse seine tuna fisheries, Fishery Bulletin, 77(2), 317-337.
  5. [5]  Cresswell, W. (2011), Predation in bird populations, Journal of Ornithology, Springer, 152(1), 251-263.
  6. [6]  Guin, L.N. (2014), Existence of spatial patterns in a predator-prey model with self- and cross-diffusion, Applied Mathematics and Computation, Elsevier, 226, 320-335.
  7. [7]  Guin, L.N. and Acharya, S. (2017), Dynamic behaviour of a reaction-diffusion predator-prey model with both refuge and harvesting, Nonlinear Dynamics, Springer, 88(2), 1501-1533.
  8. [8]  Guin, L.N. and Baek, H. (2018), Comparative analysis between prey-dependent and ratio-dependent predator-prey systems relating to patterning phenomenon, Mathematics and Computers in Simulation, Elsevier, 146, 100-117.
  9. [9]  Guin, L.N., Das, E., and Sambath, M. (2020), Pattern formation scenario through Turing instability in interacting reaction-diffusion systems with both refuge and nonlinear harvesting, Journal of Applied Nonlinear Dynamics, L $\&$ H Scientific Publishing, LLC, 9(1), 1-21.
  10. [10]  Gupta, R.P. and Chandra, P. (2013), Bifurcation analysis of modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting, Journal of Mathematical Analysis and Applications, Elsevier, 398(1), 278-295.
  11. [11]  Gupta, R.P., Chandra, P., and Banerjee, M. (2015), Dynamical complexity of a prey-predator model with nonlinear predator harvesting, Discrete $\&$ Continuous Dynamical Systems-B, American Institute of Mathematical Sciences, 15(2), 423-443.
  12. [12]  Hale, J.K. (1976), Theory of Functional Differential Equations, Springer-Verlag, New York.
  13. [13]  Han, R., Guin, L.N., and Dai, B. (2020), Cross-diffusion-driven pattern formation and selection in a modified Leslie-Gower predator-prey model with fear effect, Journal of Biological Systems, World Scientific, 28(01), 27-64.
  14. [14]  Haque, M. (2009), Ratio-dependent predator-prey models of interacting populations, Bulletin of Mathematical Biology, Springer, 71(2), 430-452.
  15. [15]  Hu, D. and Cao, H. (2017), Stability and bifurcation analysis in a predator-prey system with Michaelis-Menten type predator harvesting, Nonlinear Analysis: Real World Applications, Elsevier, 33, 58-82.
  16. [16]  Kar, T.K. and Chaudhuri, K.S. (2003), Regulation of a prey-predator fishery by taxation: a dynamic reaction model, Journal of Biological Systems, World Scientific, 11(02), 173-187.
  17. [17]  Kar, T.K. (2006), Modelling and analysis of a harvested prey predator system incorporating a prey refuge, Journal of Computational and Applied Mathematics, Elsevier, 185(1), 19-33.
  18. [18]  Layek, G.C. (2015), An Introduction to Dynamical System and Chaos, Springer.
  19. [19]  Leslie, P.H. and Gower, J.C. (1960), The properties of a stochastic model for the predator-prey type of interaction between two species, Biometrika, JSTOR, 47(3-4), 219-234.
  20. [20]  Lynch, S. (2013), Dynamical System with Application using MATLAB, Springer.
  21. [21]  Marsden, J.E. and Hoffman, M.J. (1993), Elementary Classical Analysis, Macmillan.
  22. [22]  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, World Scientific, 13(04), 157-177.
  23. [23]  Murray, J.D. (2003), ph{Mathematical Biology I: Spatial Models and Biomedical Applications, Springer-Verlag}, New York.
  24. [24]  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, World Scientific, 28(01), 1850009.
  25. [25]  Perko, L. (2001), Differential Equations and Dynamical Systems, Springer.
  26. [26]  Seo, G. and DeAngelis, D.L. (2011), A predator-prey model with a Holling type I functional response including a predator mutual interference, Journal of Nonlinear Science, Springer, 21(6), 811-833.
  27. [27]  Strogatz, S.H. (1994), Nonlinear Dynamics and Chaos: With Application to Physics, Biology, Chemistry and Engineering, Taylor and Francis, CRC Press.
  28. [28]  Suraci, J.P., Clinchy, M., Dill, L.M., Roberts, D., and Zanette, L.Y. (2016), Fear of large carnivores causes a trophic cascade, Nature Communications, Springer, 7(1), 1-7.
  29. [29]  Volterra, V. (1927), Variazioni e fluttuazioni del numero dindividui in specie animali conviventi, C. Ferrari.
  30. [30]  Wang, X., Zanette, L., and Zou, X. (2016), Modelling the fear effect in predator-prey interactions, Journal of Mathematical Biology, Springer, 73(5), 1179-1204.

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