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Dynamics of a discrete ratio-dependent predator-prey system incorporating harvesting

박성진|이상민|서정욱|현다경|백헌기|하준수
영남수학회 (Youngnam Mathematical Society)|2015.09|East Asian Mathematical Journal|제31권 제5호|pp. 743-751|DOI http://dx.doi.org/10.7858/eamj.2015.055

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키워드

stabilitya discrete ratio-dependent predator-prey systemharvesting effecta cycleperiodic doubling bifurcation
주제분류수학

초록

In this paper, we consider a discrete ratio-dependent predator-prey system with harvesting effect. In order to investigate dynamical behaviors of this system, first we find out all fixed points of the system and then classify their stabilities by using their Jacobian matrices and local stability method. Next, we display some numerical examples to substantiate theoretical results and finally, we show numerically, by means of a bifurcation diagram, that various dynamical behaviors including cycles, periodic doubling bifurcation and chaotic bands can be existed.

Abstract

In this paper, we consider a discrete ratio-dependent predator-prey system with harvesting effect. In order to investigate dynamical behaviors of this system, first we find out all fixed points of the system and then classify their stabilities by using their Jacobian matrices and local stability method. Next, we display some numerical examples to substantiate theoretical results and finally, we show numerically, by means of a bifurcation diagram, that various dynamical behaviors including cycles, periodic doubling bifurcation and chaotic bands can be existed.

참고문헌 (24)

  1. H. N. Agiza, "Chaotic dynamics of a discrete prey-predator model with Holling type II", Nonlinear Analysis:RWA, 10, pp.116~129 (2009)
  2. R. Arditi, "Coupling in predator-prey dynamics:ratio-dependence", J. Theor. Biol., 139, pp.311~326 (1989)
  3. H. Baek, "Spatiotemporal Dynamics of a predator-prey system with linear harvesting rate", Mathematical Problems in Engineering, 2014, pp.9~ (2014)
  4. J. Chen, "Permance for a discrete ratio-dependent predator-prey system with Holling type III functional response and feedback controls", Discrete Dynamics in Nature and Society, 2013, pp.6~ (2013)
  5. G. Chen, "Analysis of stability for a discrete ratio-dependent predator-prey system", Indian J. Pure Appl. Math., 42, pp.1~26 (2011)
  6. M. Danca, "Detailed analysis of a nonlinear prey-predator model", J. Biol. Phys., 23, pp.11~20 (1997)
  7. L. Dong, "Extinction and permance of the predator-prey system with stocking of prey and harvesting of predator impulsively", Math. Meth. Appl. Sci., 29, pp.415~425 (2006)
  8. M. Fan, "Dynamics of a nonautonomous predator-preysy stem with the Beddington-DeAngelis functional response", J. of Math. Anal. and Appl., 295, pp.15~39 (2004)
  9. H. I. Freedman, "Persistence in predator-prey systems with ratio-dependent predator influence", Bulletin of Math. Biology, 55(4), pp.817~827 (1993)
  10. S. Gakkha, "Chaos in seasonally perturbed ratio-dependent prey-predator system", Chaos, Solitons and Fractals, 15, pp.107~118 (2003)
  11. W. Ko, "Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge", J. of Differential Equations, 231(2), pp.534~550 (2006)
  12. L. Ling, "Dynamics of a Ivlev-type predator-prey system with constant rate harvesting", Chaos, Solitons & Fractals, 41(4), pp.2139~2153 (2009)
  13. B. Liu, "Dynamic complexities in a Lotka-Volterra predator-prey model concerning impulsive control strategy", Int. J. of Bifur. and Chaos, 15(2), pp.517~531 (2005)
  14. X. Liu, "Complex dynamic behaviors of a discrete-time predator-prey system", Chaos, Solitons and Fractals, 32, pp.80~94 (2007)
  15. X. Liu, "Bifurcation of a ratio-dependent Holling-Tanner system with refuge and constant havesting", Abstract and Applied Analysis, 2013, pp.1~10 (2013)
  16. S. Ruan, "Golbal analysis in a predator-prey sytem with non-monotonic functional response", SIAM J. Appl. Math., 61(4), pp.1445~1472 (2001)
  17. E. Saez, "Dynamics of a predator-prey model", SIAM J. Appl. Math., 59(5), pp.1867~1878 (1999)
  18. Q. Wang, "Dynamics of a class of nonautonomous semi-ratio-dependent predator-prey systems with functional responses", J. of Math. Analy. and Appl., 278, pp.443~471 (2003)
  19. W.Wang, "Spatiotemporal complexity of a ratio-dependent predator-prey system", Physical Review E, 75, pp.051913(9)~ (2007)
  20. T.Wu, "Dynamic Behaviors of a discrete two species predator-prey system incorporationg harvesting", Discrete Dynamics in Nature and Society, 2012, pp.12~ (2012)
  21. M. Xi, "Hopf bifurcation and non-hyperbolic equilibrium in a ratio-dependent predatorprey model with linear harvesting rate: Analysis and computation", Mathematical and Computer Modelling, 50 (2009)
  22. D. Xiao, "Bifurcation of a ratio-dependent predator-prey system with constant rate harvesting", SIAM J. Appl. Math., 65(3), pp.737~753 (2005)
  23. D. Xiao, "Dynamics in a ratio-dependent predator-prey model with predator harvesting", J. Math. Anal. Appl., 324, pp.14~29 (2006)
  24. X. Zhuo, "Global asymptotic stability for a two-species discrete ratio-depdendent predator-prey system", International Journal of Biomathematics, 6(1), pp.1250064-1~1250064-16 (2013)

관련 논문AI추천

Dynamical Behaviors of a Discrete Predator-Prey System with Beddington-DeAngelis Functional Response백헌기, 최윤호경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제1호Complex Dynamic Behaviors of an Impulsively Controlled Predator-prey System with Watt-type Functional Response백헌기경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제3호On the Dynamical Behavior of a Two-Prey One-Predator System with Two-Type Functional Responses백헌기경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제4호Extinction and Permanence of a Holling I Type Impulsive Predator-prey Model정창도, Hunki Baek경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제4호Delayed Dynamics of Prey-Predator System with Distinct Functional ResponsesS. Vijaya, V. Madhusudanan경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2017 · 제57권 제2호Bifurcation of a predator-prey system with generation delay and habitat complexityHaopeng Tang, Shufan Wang, Tingting Wang, Zhihui Ma대한수학회 · 대한수학회지2018 · 제55권 제1호

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