Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 46
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Li, Haiyin and She, Zhikun 2016. Dynamics of a non-autonomous density-dependent predator–prey model with Beddington–DeAngelis type. International Journal of Biomathematics, Vol. 09, Issue. 04, p. 1650050.


    Zhang, Xueli Huang, Yehui and Weng, Peixuan 2016. Stability and bifurcation of a predator–prey model with disease in the prey and temporal–spatial nonlocal effect. Applied Mathematics and Computation, Vol. 290, p. 467.


    Diop, Oumar Moussaoui, Ali and Sène, Abdou 2015. Positive periodic solution of an augmented predator-prey model with seasonal harvest of prey and migration of predator. Journal of Applied Mathematics and Computing,


    Li, Haiyin and She, Zhikun 2015. Uniqueness of periodic solutions of a nonautonomous density-dependent predator–prey system. Journal of Mathematical Analysis and Applications, Vol. 422, Issue. 2, p. 886.


    Bai, Ling Li, Jingshi Zhang, Kai and Zhao, Wenju 2014. Analysis of a stochastic ratio-dependent predator–prey model driven by Lévy noise. Applied Mathematics and Computation, Vol. 233, p. 480.


    Du, Zengji and Feng, Zhaosheng 2014. Periodic solutions of a neutral impulsive predator–prey model with Beddington–DeAngelis functional response with delays. Journal of Computational and Applied Mathematics, Vol. 258, p. 87.


    Makarenkov, Oleg 2014. Topological degree in the generalized Gause prey–predator model. Journal of Mathematical Analysis and Applications, Vol. 410, Issue. 2, p. 525.


    Song, Yongli and Zou, Xingfu 2014. Bifurcation analysis of a diffusive ratio-dependent predator–prey model. Nonlinear Dynamics, Vol. 78, Issue. 1, p. 49.


    Song, Yongli Peng, Yahong and Zou, Xingfu 2014. Persistence, Stability and Hopf Bifurcation in a Diffusive Ratio-Dependent Predator–Prey Model with Delay. International Journal of Bifurcation and Chaos, Vol. 24, Issue. 07, p. 1450093.


    Zhang, Xueli Huang, Yehui and Weng, Peixuan 2014. Permanence and stability of a diffusive predator–prey model with disease in the prey. Computers & Mathematics with Applications, Vol. 68, Issue. 10, p. 1431.


    Ali, N. and Jazar, M. 2013. Global dynamics of a modified Leslie-Gower predator-prey model with Crowley-Martin functional responses. Journal of Applied Mathematics and Computing, Vol. 43, Issue. 1-2, p. 271.


    Ding, Xiaoquan Wang, Chunwei and Chen, Peng 2013. Permanence for a two-species Gause-type ratio-dependent predator–prey system with time delay in a two-patch environment. Applied Mathematics and Computation, Vol. 219, Issue. 17, p. 9099.


    Ding, Xiaoquan Liu, Hongyuan and Wang, Fengye 2013. Periodic Solutions for Gause-Type Ratio-Dependent Predator-Prey Systems with Delays on Time Scales. Discrete Dynamics in Nature and Society, Vol. 2013, p. 1.


    Liu, Zhenjie 2013. Dynamics of positive solutions to SIR and SEIR epidemic models with saturated incidence rates. Nonlinear Analysis: Real World Applications, Vol. 14, Issue. 3, p. 1286.


    Nobile, Amelia G. Pirozzi, Enrica Caputo, Luigia and Buonocore, Aniello 2013. A non-autonomous stochastic predator-prey model. Mathematical Biosciences and Engineering, Vol. 11, Issue. 2, p. 167.


    Wu, Haihui and Zhou, Yan 2013. Periodic Solutions of a Nonautonomous Plant-Hare Model with Impulses. Discrete Dynamics in Nature and Society, Vol. 2013, p. 1.


    Gu, Xiang and Xia, Yong-Hui 2012. Stability analysis in a nonlinear ecological model. Journal of Applied Mathematics and Computing, Vol. 39, Issue. 1-2, p. 189.


    Xia, Yong-Hui Gu, Xiang Wong, Patricia J. Y. and Abbas, Syed 2012. Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System. Abstract and Applied Analysis, Vol. 2012, p. 1.


    Zhou, Tiejun Zhang, Xiaolan and Wang, Min 2012. Multiple Periodic Solutions of a Ratio-Dependent Predator-Prey Discrete Model. Discrete Dynamics in Nature and Society, Vol. 2012, p. 1.


    Tang, Mei-Lan and Liu, Xin-Ge 2011. Positive periodic solution for ratio-dependent n-species discrete time system. Applications of Mathematics, Vol. 56, Issue. 6, p. 577.


    ×
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 133, Issue 1
  • February 2003, pp. 97-118

Dynamics of a non-autonomous ratio-dependent predator—prey system

  • Meng Fan (a1), Qian Wang (a1) and Xingfu Zou (a2)
  • DOI: http://dx.doi.org/10.1017/S0308210500002304
  • Published online: 12 July 2007
Abstract

We investigate a non-autonomous ratio-dependent predator–prey system, whose autonomous versions have been analysed by several authors. For the general non-autonomous case, we address such properties as positive invariance, permanence, non-persistence and the globally asymptotic stability for the system. For the periodic and almost-periodic cases, we obtain conditions for existence, uniqueness and stability of a positive periodic solution, and a positive almost-periodic solution, respectively.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×