Permanence and extinction for a delayed periodic predator-prey system
Abstract
In this paper, the permanence, extinction and periodic solution of a delayedperiodic predator-prey system with Holling type IV functional response and stagestructure for prey is studied. By means of comparison theorem, some sufficient andnecessary conditions are derived for the permanence of the system.
Keywords
Full Text:
PDFReferences
Z. Ma, Z.Li, S. Wang, T. Li, F. Zhang, Permanence of a predator-prey system with stage structure and time delay, Appl. Math. Comput. 201 (2008) 65-71.
R. Xu, M.A.J. Chaplain, F.A. Davidson, Persistence and global stability of a ratio-dependent predator-prey model with stage structure, Appl. Math. Comput. 158 (2004) 729-744.
Z. Li, L. Chen, J. Huang, Permanence and periodicity of a delayed ratio-dependent predator-prey model with Holling type functional response and stage structure, J. Comput. Appl. Math 233 (2009) 173-187.
F. Chen, M. You, Permanence, extinction and periodic solution of the predator-prey system with Beddington-DeAngelis functional response and stage structure for prey, Nonl. Anal.: RWA 9 (2008) 207-221.
J. Cui, Permanence of predator-prey system with periodic coefficients, Mat. Comput. Model. 42 (2005) 87-98.
S. Chen, F.Wang, T. Young, Positive periodic solution of two-species ratio-dependent predator-prey system with time delay in two-patch environment, Appl. Math. Comput. 150 (2004) 737-748.
Z. Zhang, J. Luo, Multiple periodic solutions of a delayed predator-prey system with stage structure for the predator, Nonl. Anal.: RWA 11 (2010) 4109-4120.
R. Xu, M.A.J. Chaplain, F.A. Davidson, Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure, J. Math. Anal. Appl. 303 (2005) 602-621.
C. Huang, M. Zhao, H. Huo, Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey, Abstract and Applied Analysis,Volume 2008, Article ID 371632, 15 pages.
C. Huang, M. Zhao, L. Zhao, Permanence of periodic predator-prey system with two predators and stage structure for prey, Nonl. Anal.: RWA 11 (2010) 503-514.
D. Xiao, W. Li, M. Han, Dynamics in a ratio-dependent predator-prey model with predator harvesting, J. Math. Anal. Appl. 324 (2006) 14-29.
S. Hsu, T. Hwang, Y. Kuang, Rich dynamics of a ratio-dependent one prey two predators model, J. Math. Biol. 43 (2001) 377-396.
X. Zhang, Y. Tang, R. Scherer, Stability analysis of equilibrium manifolds for a two-predators one-prey model, Tsinghua Science and Technology. 11 (2006) 739-744.
B. Dubey, R.K. Upadhyay, Persistence and extinction of one-prey and two-predators system, Nonlinear Analysis: Modelling and Control, 9 (2004) 307-329.
J.A. Cui, L.S. Chen, W. Wang, The effect of dispersal on population growth with stage-structure, Comput. Math. Appl. 39 (2000) 91-102.
X.Q. Zhao, The qualitative analysis of N-species Lotka-Volterra periodic competition systems, Math. Comput. Modelling 15 (1991) 3-8.
Z. Teng, L. Chen, The positive periodic slotions in periodic Kolmogorov type systems with delays, Acta. Math. Appl. Sinica, 22 (1999) 446-456 (in chinese).
Refbacks
- There are currently no refbacks.
Copyright (c) 2015 Journal of Progressive Research in Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Copyright © 2016 Journal of Progressive Research in Mathematics. All rights reserved.
ISSN: 2395-0218.
For any help/support contact us at editorial@scitecresearch.com, jprmeditor@scitecresearch.com.