ZHANG Lili.The Turing instability in a class of predator-prey system with constant harvesting rate[J].Journal of Yanbian University,2018,44(04):306-309.
一类具有常数收获率的捕食者-食饵系统的Turing不稳定性
- Title:
- The Turing instability in a class of predator-prey system with constant harvesting rate
- 关键词:
- 捕食者-食饵模型; 收获率; 扩散; Turing不稳定性
- Keywords:
- predator-prey models; harvesting rate; diffusion; Turing instability
- 分类号:
- O175.8
- 文献标志码:
- A
- 摘要:
- 讨论了一类具有常数收获率的捕食者-食饵系统.利用Hopf分歧定理得到了ODE模型正平衡点的渐近稳定性和PDE模型的Turing不稳定性.
- Abstract:
- In this paper, a class of predator-prey system with constant harvesting rate is discussed. The asymptotic stability of the positive equilibrium point of the ODE model and the Turing instability of the PDE model are obtained by using the Hopf bifurcation theorem.
参考文献/References:
[1] Xiao D, Ruan S. Bogdanov-Takens bifurcations in predator-prey systems with constant-rate harvesting[J]. Fields Institute Communications, 1999,21:493-506.
[2] Gupta R P, Chandra P. Bifurcation analysis of modified Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting[J]. Journal of Mathematical Analysis & Applications, 2013,398(1):278-295.
[3] Sen M, Srinivasu PDN, Banerjee M. Global dynamics of an additional food provided predator-prey system with constant harvest in predators[J]. Applied Mathematics & Computation, 2015,250:193-211.
[4] Lee J, Baek H. Dynamics of a Beddington-DeAngelis type predator-prey system with constant rate harvesting[J]. Electronic Journal of Qualitative Theory of Differential Equations, 2017,2017(1):1-20.
[5] Jana S, Guria S, Das U, et al. Effect of harvesting and infection on predator in a prey-predator system[J]. Nonlinear Dynamics, 2015,81(1/2):1-14.
[6] Baek H. Spatiotemporal dynamics of a predator-prey system with linear harvesting rate[J]. MathematicalProblems in Engineering, 2014,2014(3):1-9.
[7] Wei C, Chen L. Periodic solution and heteroclinic bifurcation in a predator-prey system with Allee effect and impulsive harvesting[J]. Nonlinear Dynamics, 2014,76(2):1109-1117.
[8] Faria T. Hopf bifurcation for a delayed predator-prey model and the effect of diffusion[J]. Birkhäuser Boston, 2001,254(2):433-463.
[9] Tang X, Song Y. Bifurcation analysis and Turing instability in a diffusive predator-prey model with herd behavior and hyperbolic mortality[J]. Chaos Solitons & Fractals the Interdisciplinary Journal of Nonlinear Science & Nonequilibrium & Complex Phenomena, 2015,81:303-314.
[10] Tang X, Song Y, Zhang T. Turing-Hopf bifurcation analysis of a predator-prey model with herd behavior and cross-diffusion[J]. Nonlinear Dynamics, 2016,86(1):1-17.
[11] Song Y, Zou X. Spatiotemporal dynamics in a diffusive ratio-dependent predator-prey model near a Hopf-Turing bifurcation point[J]. Computers & Mathematics with Applications, 2014,67(10):1978-1997.
[12] Ghorai S, Poria S. Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity[J]. Chaos Solitons & Fractals, 2016,91:421-429.
相似文献/References:
[1]张丽丽,麻作军.一类带收获率的捕食者- 食饵扩散模型的稳定性[J].延边大学学报(自然科学版),2022,(04):336.
ZHANG Lili,MA Zuojun.Stability in a Lotka -Volterra predator - prey model with diffusion and harvesting rate[J].Journal of Yanbian University,2022,(04):336.
备注/Memo
收稿日期: 2018-05-17
作者简介: 张丽丽(1985—),女,讲师,研究方向为偏微分方程与生物数学.