دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات44
تعداد شماره‌ها1,312
تعداد مقالات16,137
تعداد مشاهده مقاله52,723,155
تعداد دریافت فایل اصل مقاله15,390,268
Jalilian, Yaghoub, Farshid, Marzieh. (1403). Hopf bifurcation and Turing instability in a cross-diffusion prey-predator system with group defense behavior. سامانه مدیریت نشریات علمی, 13(1), 294-306. doi: 10.22034/cmde.2024.59327.2522
Yaghoub Jalilian; Marzieh Farshid. "Hopf bifurcation and Turing instability in a cross-diffusion prey-predator system with group defense behavior". سامانه مدیریت نشریات علمی, 13, 1, 1403, 294-306. doi: 10.22034/cmde.2024.59327.2522
Jalilian, Yaghoub, Farshid, Marzieh. (1403). 'Hopf bifurcation and Turing instability in a cross-diffusion prey-predator system with group defense behavior', سامانه مدیریت نشریات علمی, 13(1), pp. 294-306. doi: 10.22034/cmde.2024.59327.2522
Jalilian, Yaghoub, Farshid, Marzieh. Hopf bifurcation and Turing instability in a cross-diffusion prey-predator system with group defense behavior. سامانه مدیریت نشریات علمی, 1403; 13(1): 294-306. doi: 10.22034/cmde.2024.59327.2522

Hopf bifurcation and Turing instability in a cross-diffusion prey-predator system with group defense behavior

Computational Methods for Differential Equations
مقاله 22، دوره 13، شماره 1، فروردین 2025، صفحه 294-306    اصل مقاله (1.85 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.59327.2522
نویسندگان
Yaghoub Jalilian* ؛ Marzieh Farshid
Department of Mathematics, Razi University, Kermanshah, Iran.
چکیده
This paper is concerned with a cross-diffusion prey-predator system in which the prey species is equipped with the group defense ability under the Neumann boundary conditions. The tendency of the predator to pursue the prey is expressed in the cross-diffusion coefficient, which can be positive, zero, or negative. We first select the environmental protection of the prey population as a bifurcation parameter. Next, we discuss the Turing instability and the Hopf bifurcation analysis on the proposed cross-diffusion system. We show that the system without cross-diffusion is stable at the constant positive stationary solution but it becomes unstable when the cross-diffusion appears in the system. Furthermore, the stability of bifurcating periodic solutions and the direction of Hopf bifurcation are examined. 
کلیدواژه‌ها
Turing instability؛ Prey-predator model؛ Hopf bifurcation؛ Cross-diffusion
مراجع
  • [1] M. F. Carfora and I. Torcicollo, Cross-diffusion-driven instability in a predator-prey system with fear and group defense, Mathematics, 8(8) (2020), 1244.
  • [2] M. Farshid and Y. Jalilian, Steady state bifurcation in a cross diffusion prey-predator model, Computational Methods for Differential Equations, 11(2) (2023), 254–262.
  • [3] H. I. Freedman and G. S. Wolkowicz, Predator-prey systems with group defence: the paradox of enrichment revisited, Bulletin of Mathematical Biology, 48(5-6) (1986), 493–508.
  • [4] S. Fu and H. Zhang, Effect of hunting cooperation on the dynamic behavior for a diffusive Holling type II predatorprey model, Communications in Nonlinear Science and Numerical Simulation, 99 (2021), 105807.
  • [5] R. Han and B. Dai, Cross-diffusion induced Turing instability and amplitude equation for a toxic-phytoplanktonzooplankton model with nonmonotonic functional response, International Journal of Bifurcation and Chaos, 27(6) (2017), 1750088.
  • [6] B. D. Hassard, N. D. Kazarinoff, and Y. Wan, Theory and Application of Hopf Bifurcation, Cambridge University Press, Cambridge, MA 1981.
  • [7] V. Kumar and N. Kumari, Bifurcation study and pattern formation analysis of a tritrophic food chain model with group defense and Ivlev-like nonmonotonic functional response, Chaos, Solitons and Fractals, 147 (2021), 110964.
  • [8] S. Li, Z. Li, and B. Dai, Stability and Hopf bifurcation in a prey-predator model with memory-based diffusion, Discrete and Continuous Dynamical Systems-B, 27(11) (2022), 6885–6906.
  • [9] T. Ma and X. Meng, Global analysis and Hopf-bifurcation in a cross-diffusion prey-predator system with fear effect and predator cannibalism, Mathematical Biosciences and Engineering, 19(6) (2022), 6040–6071.
  • [10] R. R. Patra, S. Kundu, and S. Maitra, Effect of delay and control on a predator-prey ecosystem with generalist predator and group defence in the prey species, The European Physical Journal Plus, 137(1) (2022), 28.
  • [11] R. R. Patra, S. Maitra, and S. Kundu, Stability, bifurcation and control of a predator-prey ecosystem with prey herd behaviour against generalist predator with gestation delay, arXiv preprint arXiv:2103.16263 (2021).
  • [12] T. S. Shivam and M. Kumar, Spatiotemporal dynamical analysis of a predator-prey system with fear and group defense in prey, Journal of Biological Systems, 30(2) (2022), 387–422.
  • [13] J. Shi, Z. Xie and K. Little, Cross-diffusion induced instability and stability in reaction-diffusion systems, J. Appl. Anal. Comput, 1(1) (2011), 95–119.
  • [14] R. Su and C. Zhang, The generation mechanism of Turing-pattern in a Tree-grass competition model with cross diffusion and time delay, Mathematical Biosciences and Engineering, 19(12) (2022), 12073–12103.
  • [15] J. S. Tener, Muskoxen in Canada: a biological and taxonomic review, Canadian Wildlife Service, 1965.
  • [16] A. M. Turing, The chemical basis of morphogenesis, Bulletin of mathematical biology, 52 (1990), 153–197.
  • [17] D. Xiao and S. Ruan, Global analysis in a predator-prey system with nonmonotonic functional response, SIAM J. Appl. Math., 61(4) (2001), 1445–1472.
  • [18] Z. Xie, Cross-diffusion induced Turing instability for a three species food chain model, Journal of Mathematical Analysis and Applications, 388(1) (2012), 539–547.
  • [19] X. P. Yan, Y. J. Ding, and C. H. Zhang, Dynamics analysis in a Gierer-Meinhardt reaction-diffusion model with homogeneous Neumann boundary condition, International Journal of Bifurcation and Chaos, 29(9) (2019), 1930025.
  • [20] F. Yi, Turing instability of the periodic solutions for reaction-diffusion systems with cross-diffusion and the patch model with cross-diffusion-like coupling, Journal of Differential Equations, 281 (2021), 379–410.
  • [21] F. Q. Yi, J. J. Wei, and J. P. Shi, Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system, J. Differential Equations, 246(5) (2009), 1944–1977.
  • [22] C. Zhang, R. Wu, and M. Chen, Hopf bifurcation in a delayed predator-prey system with general group defence for prey, Journal of Applied Analysis and Computation, 11(2) (2021), 810–840.
  • [23] M. Zhu, J. Li, and X. Lian, Pattern dynamics of cross diffusion predator-prey system with strong Allee effect and hunting cooperation, Mathematics, 10(17) (2022), 3171.
آمار
تعداد مشاهده مقاله: 133
تعداد دریافت فایل اصل مقاله: 199


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب