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The bifurcation analysis of an eco-toxicant model with anti-predator behavior | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 148، دوره 13، شماره 1، خرداد 2022، صفحه 1785-1801 اصل مقاله (603.62 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.5798 | ||
| نویسندگان | ||
| Huda Salah Kareem* 1؛ Azhar Abbas Majeed2 | ||
| 1Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq | ||
| 2Department of mathematics, College of Science, University of Baghdad, Baghdad, Iraq | ||
| تاریخ دریافت: 22 مهر 1400، تاریخ بازنگری: 04 آذر 1400، تاریخ پذیرش: 09 آذر 1400 | ||
| چکیده | ||
| In this study, the mathematical model of four differential equations for organisms that describe the effect of anti-predation behavior, age stage and toxicity have been analyzed. Local bifurcation and Hopf bifurcation have been studied by changing a parameter of a model to study the dynamic behavior determined by bifurcation curves and the occurrence states of bifurcation saddle node, transcritical and pitch fork bifurcation. The potential equilibrium point at which Hopf bifurcation occurs has been determined and the results of the bifurcation behavior analysis have been fully presented using numerical simulation. | ||
| کلیدواژه‌ها | ||
| Prey-Predator؛ Local bifurcation؛ Global bifurcation؛ Hopf bifurcation | ||
| مراجع | ||
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[1] P. Blanchard, R.L Devaney and G.R. Hall, Differential Equations, Cengage Learning Inc., 2006. [2] Q. Chen, Z. Teng and Z. Hu, Bifurcation and control for a discrete-time prey-predator model with Holling–IV functional response, J. Appl. Math. Comput. Sci. 23 (2013) 247–261. [3] J.U. Henri Poincare. L’Equilibre d’une masse fluide anime d’un mouvement de rotation , Acta Math. 7 (1885) 259–380. [4] A.J. Kadhim and A.A. Majeed, The impact of toxicant on the food chain ecological model, AIP Conf. Proc. 2292 (2020) 1–14. [5] E.M. Kafl and A.A. Majeed, The dynamics and analysis of stage-structured predator-prey model involving disease and refuge in prey population, J. Phys. Conf. Ser. 1530 (2020) 1–24. [6] H. S. Kareem and A. A. Majeed, Qualitative study of an eco-toxicant model with anti-predator behavior, Int. J. Nonlinear Anal. Apple, 12 (2021) 1861-1882. [7] M.A. Lafta and A.A. Majeed, The food web prey-predator model with toxin, AIP Conf. Proc. 2292 (2020) 1–11. [8] A.A. Majeed and A.J. Kadhim, The bifurcation analysis and persistences of food chain ecological model with toxicant, J. Phys. Conf. Ser. 1818 (2021) 1–13. [9] A.A. Majeed and M.A. Lafta, The bifurcation analysis of food web prey-predator model with toxin, J. Phys. Conf. Ser. 1897 (2021) 1–18. [10] A.A. Majeed and M.H. Ismaeeb, The bifurcation analysis of prey-predator model in the presence of stage-structured with harvesting and toxicity, J. Southwest Jiao Tong Univ. 54(6) (2019). [11] A.A. Majeed, Local bifurcation and persistence of an ecological system consisting of a predator and stage-structured prey, Iraqi J. Sci. 54(3) (2013) 696–705. [12] S.G. Mortoja, P. Panja and S.K. Mondal, Dynamics of a predator-prey model with stage-structure on both species and anti-predator behavior, Inf. Medic. Unlocked 10 (2018) 50–57. [13] B. Pirayesh, A. Pazirandeh and M. Akbari, Local bifurcation analysis in nuclear reactor dynamics by Sotomayor’s theorem, Ann. Nuclear Energy 94 (2016) 716. [14] M.R. Roussel, Introduction to Bifurcation, Nonlinear Dynamics a hands-on Introductory Survey, (2005) 1-19. [15] A. Verdugo and R. Rand, Hopf bifurcation in a DDE model of gene expression, Commun. Nonlinear Sci. Numerical Simul. 13 (2008) 235–242. | ||
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