Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

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

1. Department of Mathematics and Applications, University of Naples Federico II, via Cintia, I-80126 Naples
2. Department of Mathematics, University of Lecce, via Provinciale Lecce-Arnesano, I-73100 Lecce

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.
  Article Metrics

Keywords stage structure; cannibalism; predator-prey models; oscillations.; Hopf bifurcation

Citation: Bruno Buonomo, Deborah Lacitignola. On the stabilizing effect of cannibalism in stage-structured population models. Mathematical Biosciences and Engineering, 2006, 3(4): 717-731. doi: 10.3934/mbe.2006.3.717


This article has been cited by

  • 1. Brent T. Boscarino, Lars G. Rudstam, Monica A. Minson, Emily E. Freund, Laboratory-derived light and temperature preferences of juvenile mysid shrimp, Mysis diluviana, Journal of Great Lakes Research, 2010, 36, 4, 699, 10.1016/j.jglr.2010.06.012
  • 2. Aladeen Basheer, Emmanuel Quansah, Suman Bhowmick, Rana D. Parshad, Prey cannibalism alters the dynamics of Holling–Tanner-type predator–prey models, Nonlinear Dynamics, 2016, 85, 4, 2549, 10.1007/s11071-016-2844-8
  • 3. Subhendu Chakraborty, J. Chattopadhyay, Effect of cannibalism on a predator–prey system with nutritional value: a model based study, Dynamical Systems, 2011, 26, 1, 13, 10.1080/14689367.2010.491076
  • 4. Shaohong Cai, Jianjun Jiao, Limei Li, Dynamics of a pest management predator–prey model with stage structure and impulsive stocking, Journal of Applied Mathematics and Computing, 2016, 52, 1-2, 125, 10.1007/s12190-015-0933-3
  • 5. Suzanne L. Robertson, Shandelle M. Henson, Timothy Robertson, J. M. Cushing, A matter of maturity: To delay or not to delay? Continuous-time compartmental models of structured populations in the literature 2000-2016, Natural Resource Modeling, 2018, 31, 1, e12160, 10.1111/nrm.12160
  • 6. Aladeen Al Basheer, Rana D. Parshad, Emmanuel Quansah, Shengbin Yu, Ranjit Kumar Upadhyay, Exploring the dynamics of a Holling–Tanner model with cannibalism in both predator and prey population, International Journal of Biomathematics, 2018, 11, 01, 1850010, 10.1142/S1793524518500109
  • 7. Jianjun Jiao, Shaohong Cai, Lansun Chen, Dynamical behaviors of a biological management model with impulsive stocking juvenile predators and continuous harvesting adult predators, Journal of Applied Mathematics and Computing, 2011, 35, 1-2, 483, 10.1007/s12190-009-0372-0
  • 8. Aladeen Al Basheer, Jingjing Lyu, Adom Giffin, Rana D. Parshad, The “Destabilizing” Effect of Cannibalism in a Spatially Explicit Three-Species Age Structured Predator-Prey Model, Complexity, 2017, 2017, 1, 10.1155/2017/3896412
  • 9. Yunfeng Jia, Yi Li, Jianhua Wu, Effect of predator cannibalism and prey growth on the dynamic behavior for a predator-stage structured population model with diffusion, Journal of Mathematical Analysis and Applications, 2017, 449, 2, 1479, 10.1016/j.jmaa.2016.12.036
  • 10. B. Buonomo, D. Lacitignola, S. Rionero, Effect of prey growth and predator cannibalism rate on the stability of a structured population model, Nonlinear Analysis: Real World Applications, 2010, 11, 2, 1170, 10.1016/j.nonrwa.2009.01.053
  • 11. Jianquan Li, Xue Zhu, Xiaolin Lin, Jia Li, Impact of cannibalism on dynamics of a structured predator-prey system, Applied Mathematical Modelling, 2019, 10.1016/j.apm.2019.09.022
  • 12. Meijun Chen, Shengmao Fu, Xiaoli Yang, Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with Cannibalism, Complexity, 2020, 2020, 1, 10.1155/2020/1265798
  • 13. Muhammad Sajjad Shabbir, Qamar Din, Khalil Ahmad, Asifa Tassaddiq, Atif Hassan Soori, Muhammad Asif Khan, Stability, bifurcation, and chaos control of a novel discrete-time model involving Allee effect and cannibalism, Advances in Difference Equations, 2020, 2020, 1, 10.1186/s13662-020-02838-z

Reader Comments

your name: *   your email: *  

Copyright Info: 2006, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved