1,740
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

Complex behaviour in four species food-web model

, &
Pages 440-456 | Received 02 Aug 2010, Accepted 25 Aug 2011, Published online: 27 Sep 2011

References

  • Abrams , P. A. and Roth , J. D. 1994 . The effects of enrichment of three-species food chains with nonlinear functional responses . Ecology , 75 ( 4 ) : 1118 – 1130 .
  • Andronov , A. A. 1973 . Qualitative Theory of Second-Order Dynamic Systems , New York : Halsted Press .
  • Arrowsmith , D. K. 1990 . An Introduction to Dynamical Systems , Cambridge : Cambridge University Press .
  • Butler , G. , Freedman , H. I. and Waltman , P. 1986 . Uniformly persistent systems . Proc. Amer. Math. Soc. , 96 : 425 – 430 .
  • Angelis , D. L. 1975 . Stability and connectance in food web models . Ecology , 56 ( 1 ) : 238 – 243 .
  • El-Owaidy , H. and Ammar , A. A. 1986 . Mathematical analysis of a food-web model . Math. Biosci. , 81 ( 2 ) : 213 – 227 .
  • El-Owaidy , H. , Ragab , A. A. and Ismail , M. 2001 . Mathematical analysis of a food-web model . Appl. Math. Comput. , 121 : 155 – 167 .
  • Freedman , H. I. 1980 . Deterministic Mathematical Models in Population Ecology , New York : Marcel Dekker .
  • Freedman , H. I. and Hongshun , Q. 1988 . Interactions leading to persistence in predator–prey systems with group defence . Bull. Math. Biol. , 50 ( 5 ) : 517 – 530 .
  • Freedman , H. I. and Ruan , S. 1995 . Uniform persistence in functional differential equations . J. Differential Equations , 115 : 173 – 192 .
  • Freedman , H. I. and Waltman , P. 1984 . Persistence in models of three interacting predator–prey populations . J. Math. Biosci. , 68 : 213 – 231 .
  • Gakkhar , S. and Naji , R. K. 2002 . Chaos in three species ratio dependent food chain . Chaos Solitons and Fractals , 14 ( 5 ) : 771 – 778 .
  • Gakkhar , S. and Naji , R. K. 2003 . On a food web consisting of a specialist and a generalist predator . J. Biol. Syst. , 11 ( 4 ) : 365 – 376 .
  • Gakkhar , S. and Naji , R. K. 2003 . Chaos in seasonally perturbed ratio-dependent prey–predator system . Chaos Solitons and Fractals , 15 ( 1 ) : 107 – 118 .
  • Gakkhar , S. and Singh , B. 2005 . Complex dynamic behavior in a food web consisting of two preys and a predator . Chaos Solitons Fractals , 24 ( 3 ) : 789 – 801 .
  • Guckenheimer , J. and Holmes , P. 1983 . Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields , 8291 New York : Springer .
  • Hastings , A. and Powell , T. 1991 . Chaos in a three-species food chain . Ecology , 72 ( 3 ) : 896 – 903 .
  • Hogeweg , P. and Hesper , B. 1978 . Interactive instruction on population interactions . Comput. Biol. Med. , 8 ( 4 ) : 319 – 327 .
  • Kumar , R. and Freedman , H. I. 1989 . A mathematical model of facultative mutualism with populations interaction in a food chain . J. Math. Biosci. , 97 : 235 – 261 .
  • May , R. M. 1973 . Stability and Complexity in Model Ecosystems , Princeton , NJ : Princeton University Press .
  • McCann , K. and Yodzis , P. 1994 . Biological conditions for chaos in a three-species food chain . Ecology , 75 ( 2 ) : 561 – 564 .
  • McCann , K. and Yodzis , P. 1995 . Bifurcation structure of a three-species food-chain model . Theor. Popul. Biol. , 48 ( 2 ) : 93 – 125 .
  • Rai , V. and Sreenivasan , R. 1993 . Period-doubling bifurcations leading to chaos in a model food chain . Ecol. Model. , 69 ( 1–2 ) : 63 – 77 .
  • Scheffer , M. 1991 . Should we expect strange attractors behind plankton dynamics – and if so, should we bother? . J. Plankton Res. , 13 ( 6 ) : 1291
  • Segel , L. 1984 . Modeling Dynamic Phenomena in Molecular and Cellular Biology , Cambridge : Cambridge University Press .
  • Takeuchi , Y. 1996 . Global Dynamical Properties of Lotka–Voltera Systems , Singapore : World Scientific .
  • Wilder , J. W. , Voorhis , N. , Colbert , J. J. and Sharov , A. 1994 . A three variable differential equation model for gypsy moth population dynamics . Ecol. Model. , 72 ( 3–4 ) : 229 – 250 .