Hopf bifurcation analysis in a stage-structure predator–prey model with two time delay

Bochen Han; Shengming Yang; Guangping Zeng

doi:10.1051/matecconf/202235503048

All issues

Volume 355 (2022)

MATEC Web Conf., 355 (2022) 03048

References

Open Access

Issue		MATEC Web Conf. Volume 355, 2022 2021 International Conference on Physics, Computing and Mathematical (ICPCM2021)


Article Number		03048
Number of page(s)		10
Section		Computing Methods and Computer Application
DOI		https://doi.org/10.1051/matecconf/202235503048
Published online		12 January 2022

Xiao-Ke Sun, Hai-Feng Huo, Cao-Chuan Ma, Hopf bifurcation and stability in predator–prey model with a stage-structure for prey, Applied Mathematics and Computation. 219 (2013) 10313–10324. [Google Scholar]
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R. Shi, L. Chen, The study of ratio-dependent predator prey model with stage-structure in the prey, Nonlinear Dyn. 58 (2009) 443–451. [Google Scholar]
Jia Liu, Cross-diffusion induced stationary patterns in a prey–predator system with parental care for predators, Applied Mathematics and Computation. 237 (2014) 176189. [Google Scholar]
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J. Roughgarden, Y. Iwasa, C. Baxter, Demographic theory for an open marine population with space-limits, Ecology 66 (1985) 54–67 [Google Scholar]
Canrong Tian, Lai Zhang, Hopf bifurcation analysis in a diffusive food-chain model with time delay, Computers and Mathematics with Applications. 66(2013)2139-2153. [Google Scholar]
S. Sen, P. Ghosh, S.S. Riaz, D.S. Ray, Time-delay-induced instabilities in reaction– diffusion systems, Phys. Rev. E 80 (2009) 046212. [Google Scholar]
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J. Cui, L. Chen, W. Wang, The effect of dispersal on population growth with stage-structure, Comput. Math. Appl. 39 (2000) 91–102 [Google Scholar]
X.Y. Song, L.S. Chen, Optimal harvesting and stability for a predator–prey system with stage structure, Acta Math. Appl. Sin. 18 (2002) 423–430. [Google Scholar]
W.D. Wang, L.S. Chen, A predator–prey system with stage structure for predator, Comput. Math. Appl. 33 (1997) 83–91. [Google Scholar]
R. Kohn, Energy-driven pattern formation, in: Proceedings of the International Congress of Mathematicians, European Mathematical Society, Madrid, 2007, pp. 1–25 [Google Scholar]

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[1] Xiao-Ke Sun, Hai-Feng Huo, Cao-Chuan Ma, Hopf bifurcation and stability in predator–prey model with a stage-structure for prey, Applied Mathematics and Computation. 219 (2013) 10313–10324. [Google Scholar]

[2] M. Agarwal, S. Devi, Persistence in a ratio-dependent predator–prey-resource model with stage structure for prey, Int. J. Biomath. 3 (2010) 313–336. [Google Scholar]

[3] W.G. Aiello, H.I. Freedman, A time-delay model of single-species growth with stage structure, Math. Biosci. 101 (1990) 139–153. [Google Scholar]

[4] R. Shi, L. Chen, The study of ratio-dependent predator prey model with stage-structure in the prey, Nonlinear Dyn. 58 (2009) 443–451. [Google Scholar]

[5] Jia Liu, Cross-diffusion induced stationary patterns in a prey–predator system with parental care for predators, Applied Mathematics and Computation. 237 (2014) 176189. [Google Scholar]

[6] W.D. Wang, Y. Takeuchi, Y. Saito, S. Nakaoka, Prey–predator system with parental care for predators, J. Theor. Biol. 241 (2006) 451–458. [Google Scholar]

[7] J. Roughgarden, Y. Iwasa, C. Baxter, Demographic theory for an open marine population with space-limits, Ecology 66 (1985) 54–67 [Google Scholar]

[8] Canrong Tian, Lai Zhang, Hopf bifurcation analysis in a diffusive food-chain model with time delay, Computers and Mathematics with Applications. 66(2013)2139-2153. [Google Scholar]

[9] S. Sen, P. Ghosh, S.S. Riaz, D.S. Ray, Time-delay-induced instabilities in reaction– diffusion systems, Phys. Rev. E 80 (2009) 046212. [Google Scholar]

[10] S.S. Lee, E.A. Gaffney, N.A.M. Monk, The Influence of Gene Expression Time Delays on Gierer-Meinhardt Pattern Formation Systems, Bull. Math. Biol. 72 (2010) 2139–2160. [Google Scholar]

[11] C.R. Tian, Delay-driven spatial patterns in a plankton allelopathic system, Chaos 22 (2010) 013129. [Google Scholar]

[12] J. Cui, L. Chen, W. Wang, The effect of dispersal on population growth with stage-structure, Comput. Math. Appl. 39 (2000) 91–102 [Google Scholar]

[13] X.Y. Song, L.S. Chen, Optimal harvesting and stability for a predator–prey system with stage structure, Acta Math. Appl. Sin. 18 (2002) 423–430. [Google Scholar]

[14] W.D. Wang, L.S. Chen, A predator–prey system with stage structure for predator, Comput. Math. Appl. 33 (1997) 83–91. [Google Scholar]

[15] R. Kohn, Energy-driven pattern formation, in: Proceedings of the International Congress of Mathematicians, European Mathematical Society, Madrid, 2007, pp. 1–25 [Google Scholar]