Periodic solution for intraguild predation system with impulsive and strong Allee effect
-
摘要:建立了具有周期系数的带脉冲和强Allee效应的集团内捕食模型；证明了模型的持久性；利用Mawhin重合度理论与分析工具，研究了该模型周期解的存在性；讨论了周期解的稳定性；得到了正周期解存在、全局稳定的充分条件，并通过数值模拟对结果的有效性进行了验证．Abstract:With strong Allee effect and a periodic coefficient, an impulsive intraguild predation model is established．Persistence of the model is proved．Existence of periodic solutions is studied using Mawhin’s coincidence degree theory and analysis tools．The stability of periodic solutions is discussed．Sufficient conditions are obtained for existence and global stability of positive periodic solutions．Validity of theoretical results is verified by numerical simulations．
-
Key words:
- intraguild predation/
- impulses/
- Allee effect/
- periodic solution
-
图 2式 (4)
$2{\text{π}}$ -周期解的${x}_{1}\left(t\right)、{x}_{2}\left(t\right)、{x}_{3}\left(t\right)$ 演化和轨线 -
[1] POLIS G A,MYERS C A,HOLT R D. The ecology and evolution of intraguild predation:potential competitors that eat each other[J]. Annual Review of Ecology and Systematics,1989,20(1):297doi:10.1146/annurev.es.20.110189.001501 [2] HSU S B,RUAN S,YANG T H. Analysis of three species Lotka-Volterra food web models with omnivory[J]. Journal of Mathematical Analysis & Applications,2015,426(2):659 [3] RUAN S. Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling[J]. Journal of Mathematical Biology,1993,31(6):633doi:10.1007/BF00161202 [4] HAUTIER L,MARTIN G S,CALLIER P,et al. Alkaloids provide evidence of intraguild predation on native coccinellids by Harmonia axyridis in the field[J]. Biological Invasions,2011,13(8):1805doi:10.1007/s10530-010-9935-0 [5] ANDERSON T L,SEMLITSCH R D. High intraguild predator density induces thinning effects on and increases temporal overlap with prey populations[J]. Population Ecology,2014,56(2):265doi:10.1007/s10144-013-0419-9 [6] RYAN D,CANTRELL R S. Avoidance behavior in intraguild predation communities:a cross-diffusion model[J]. Discrete and Continuous Dynamical Systems: Series A,2014,35(4):1641 [7] HAN R J,DAI B X,CHEN Y M. Pattern formation in a diffusive intraguild predation model with nonlocal interaction effects[J]. AIP Advances,2019,9(3):35 [8] RABAGO J F T,COLLERA J. Hopf bifurcation in a delayed intraguild predation model[J]. Southeast Asian Bulletin of Mathematics,2018,42(5):691 [9] KANG Y,WEDEKIN L. Dynamics of an intraguild predation model with generalist or specialist predator[J]. Journal of Mathematical Biology,2013,67(5):1227doi:10.1007/s00285-012-0584-z [10] JI J P,WANG L. Competitive exclusion and coexistence in an intraguild predation model with Beddington-De Angelis functional response[J]. Communications in Nonlinear Science and Numerical Simulation,2022,107:106192doi:10.1016/j.cnsns.2021.106192 [11] TRIPATHI J P,MANDAL P S,POONIA A,et al. A widespread interaction between generalist and specialist enemies:the role of intraguild predation and Allee effect[J]. Applied Mathematical Modelling,2021,89(Part 1):105 [12] BEREC L,ANGULO E,COURCHAMP F. Multiple Allee effects and population management[J]. Trends in Ecology & Evolution,2007,22(4):185 [13] COURCHAMP F, BEREC L, GASCOIGNE J. Allee effects in ecology and conservation[M]. Illustrated Edition. New York: Oxford University Press, 2009 [14] MOORING M S,FITZPATRICK T A,NISHIHIRA T T,et al. Vigilance,predation risk,and the Allee effect in desert bighorn sheep[J]. Journal of Wildlife Management,2004,68(3):519doi:10.2193/0022-541X(2004)068[0519:VPRATA]2.0.CO;2 [15] PAL P J,SAHA T. Qualitative analysis of a predator-prey system with double Allee effect in prey[J]. Chaos Solitons and Fractals,2015,73(5):36 [16] BAI D Y, KANG Y, RUAN S G, et al. Dynamics of an intraguild predation food web model with strong Allee effect in the basal prey[J]. Nonlinear Analysis: Real World Applications, 2021, 58: 103206 [17] LASHMIKANTHAM V, BAINO D D, SIMENOV P. Theorey of impulsive differential equations[M]. Singapore: World Scientific Publishing Company, 1989 [18] WANG Q,DING M M,WANG Z J,et al. Existence and attractivity of a periodic solution for an n-species Gilpin-Ayala impulsive competition system[J]. Nonlinear Analysis: Real World Applications,2010,11(4):2675doi:10.1016/j.nonrwa.2009.09.015 [19] ZHANG S W,TAN D J,CHEN L S. The periodic n-species Gilpin-Ayala competition system with impulsive effect[J]. Chaos Solitons & Fractals,2005,26(2):507 [20] FAN X M,JIANG F Q,ZHANG H N. Dynamics of multi-species competition-predator system with impulsive perturbations and Holling type III functional responses[J]. Nonlinear Analysis,2011,74(10):3363doi:10.1016/j.na.2011.02.012 [21] GAINES R E, MAWHIN J L. Coincidence degree and nonlinear differential equations[M]. New York: Springer-Verlag, 1977 [22] ZHANG J,GUI Z J. Periodic solutions of nonautonomous cellular neural networks with impulses and delays[J]. Nonlinear Analysis Real World Applications,2009,10(3):1891doi:10.1016/j.nonrwa.2008.02.029 -
下载:
点击查看大图
图(3)
计量
- 文章访问数:153
- HTML全文浏览量:84
- PDF下载量:25
- 被引次数:0
