American Institute of Mathematical Sciences

Advanced
2006, 3(4): 717-731. doi: 10.3934/mbe.2006.3.717

On the stabilizing effect of cannibalism in stage-structured population models

Bruno Buonomo 1, and  Deborah Lacitignola 2,

1. 

Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples, Italy
2. 

Department of Mathematics, University of Lecce, via Provinciale Lecce-Arnesano, I-73100 Lecce, Italy

Received  March 2006 Revised  May 2006 Published  August 2006

In this paper we give a contribution to the systematic investigation of cannibalism in predator-prey models commenced since the publication of the paper by Kohlmeier and Ebenhöh in 1995. We present a stage-structured predator-prey model and study its dynamics. We use a Hopf bifurcation analysis to prove that cycles are possible and that cannibalism suppresses these cycles; that is, when cannibalism attack rate is increased so that it passes a critical value, the coexistence steady state changes from being unstable to being stable. Numerical simulations are provided together with the mathematical analysis. Our modelling approach is based on balance arguments and a comparison with some early models which predict that a destabilizing effect of cannibalism is performed. Our results agree with the output of growth simulation for some cannibalistic copepods.
Keywords: stage structure, cannibalism, predator-prey models, oscillations., Hopf bifurcation.
Mathematics Subject Classification: 92D25, 34C2.
Citation: Bruno Buonomo, Deborah Lacitignola. On the stabilizing effect of cannibalism in stage-structured population models. Mathematical Biosciences & Engineering, 2006, 3 (4) : 717-731. doi: 10.3934/mbe.2006.3.717
[1]

Jing-An Cui, Xinyu Song. Permanence of predator-prey system with stage structure. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 547-554. doi: 10.3934/dcdsb.2004.4.547
[2]

Seong Lee, Inkyung Ahn. Diffusive predator-prey models with stage structure on prey and beddington-deangelis functional responses. Communications on Pure & Applied Analysis, 2017, 16 (2) : 427-442. doi: 10.3934/cpaa.2017022
[3]

Xinyu Song, Liming Cai, U. Neumann. Ratio-dependent predator-prey system with stage structure for prey. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 747-758. doi: 10.3934/dcdsb.2004.4.747
[4]

Zhong Li, Maoan Han, Fengde Chen. Global stability of a predator-prey system with stage structure and mutual interference. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 173-187. doi: 10.3934/dcdsb.2014.19.173
[5]

Liang Zhang, Zhi-Cheng Wang. Spatial dynamics of a diffusive predator-prey model with stage structure. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1831-1853. doi: 10.3934/dcdsb.2015.20.1831
[6]

Xiaoling Zou, Dejun Fan, Ke Wang. Stationary distribution and stochastic Hopf bifurcation for a predator-prey system with noises. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1507-1519. doi: 10.3934/dcdsb.2013.18.1507
[7]

Wei Feng, Michael T. Cowen, Xin Lu. Coexistence and asymptotic stability in stage-structured predator-prey models. Mathematical Biosciences & Engineering, 2014, 11 (4) : 823-839. doi: 10.3934/mbe.2014.11.823
[8]

Qing Zhu, Huaqin Peng, Xiaoxiao Zheng, Huafeng Xiao. Bifurcation analysis of a stage-structured predator-prey model with prey refuge. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 2195-2209. doi: 10.3934/dcdss.2019141
[9]

Xiaoyuan Chang, Junjie Wei. Stability and Hopf bifurcation in a diffusive predator-prey system incorporating a prey refuge. Mathematical Biosciences & Engineering, 2013, 10 (4) : 979-996. doi: 10.3934/mbe.2013.10.979
[10]

Jaume Llibre, Claudio Vidal. Hopf periodic orbits for a ratio--dependent predator--prey model with stage structure. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1859-1867. doi: 10.3934/dcdsb.2016026
[11]

Rui Xu. Global convergence of a predator-prey model with stage structure and spatio-temporal delay. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 273-291. doi: 10.3934/dcdsb.2011.15.273
[12]

Yuying Liu, Yuxiao Guo, Junjie Wei. Dynamics in a diffusive predator-prey system with stage structure and strong allee effect. Communications on Pure & Applied Analysis, 2020, 19 (2) : 883-910. doi: 10.3934/cpaa.2020040
[13]

Hongyong Zhao, Daiyong Wu. Point to point traveling wave and periodic traveling wave induced by Hopf bifurcation for a diffusive predator-prey system. Discrete & Continuous Dynamical Systems - S, 2020, 13 (11) : 3271-3284. doi: 10.3934/dcdss.2020129
[14]

Zuolin Shen, Junjie Wei. Hopf bifurcation analysis in a diffusive predator-prey system with delay and surplus killing effect. Mathematical Biosciences & Engineering, 2018, 15 (3) : 693-715. doi: 10.3934/mbe.2018031
[15]

Pengmiao Hao, Xuechen Wang, Junjie Wei. Global Hopf bifurcation of a population model with stage structure and strong Allee effect. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 973-993. doi: 10.3934/dcdss.2017051
[16]

Christian Kuehn, Thilo Gross. Nonlocal generalized models of predator-prey systems. Discrete & Continuous Dynamical Systems - B, 2013, 18 (3) : 693-720. doi: 10.3934/dcdsb.2013.18.693
[17]

Shanshan Chen, Jianshe Yu. Stability and bifurcation on predator-prey systems with nonlocal prey competition. Discrete & Continuous Dynamical Systems, 2018, 38 (1) : 43-62. doi: 10.3934/dcds.2018002
[18]

Hongxiao Hu, Liguang Xu, Kai Wang. A comparison of deterministic and stochastic predator-prey models with disease in the predator. Discrete & Continuous Dynamical Systems - B, 2019, 24 (6) : 2837-2863. doi: 10.3934/dcdsb.2018289
[19]

Bing Zeng, Shengfu Deng, Pei Yu. Bogdanov-Takens bifurcation in predator-prey systems. Discrete & Continuous Dynamical Systems - S, 2020, 13 (11) : 3253-3269. doi: 10.3934/dcdss.2020130
[20]

Siyu Liu, Haomin Huang, Mingxin Wang. A free boundary problem for a prey-predator model with degenerate diffusion and predator-stage structure. Discrete & Continuous Dynamical Systems - B, 2020, 25 (5) : 1649-1670. doi: 10.3934/dcdsb.2019245

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (38)
  • HTML views (0)
  • Cited by (13)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy