The dynamic complexity of a three species food chain model

In this paper, a three-species food chain model is analytically investigated on theories of ecology and using numerical simulation. Bifurcation diagrams are obtained for biologically feasible parameters. The results show that the system exhibits rich complexity features such as stable, periodic and chaotic dynamics.

[1]  Sven Sahle,et al.  A robust, locally interpretable algorithm for Lyapunov exponents , 2003 .

[2]  J. Sprott Chaos and time-series analysis , 2001 .

[3]  Andrew M. Edwards,et al.  Generic dynamics of a simple plankton population model with a non-integer exponent of closure , 2001 .

[4]  M. Varriale,et al.  A study of a three species food chain , 1998 .

[5]  M. A. Aziz-Alaoui,et al.  Analysis of the dynamics of a realistic ecological model , 2002 .

[6]  W. Schaffer Order and Chaos in Ecological Systems , 1985 .

[7]  M. Rosenstein,et al.  A practical method for calculating largest Lyapunov exponents from small data sets , 1993 .

[8]  Chris Cosner,et al.  On the Dynamics of Predator–Prey Models with the Beddington–DeAngelis Functional Response☆ , 2001 .

[9]  S. Gakkhar,et al.  Order and chaos in predator to prey ratio-dependent food chain , 2003 .

[10]  G. Lawson,et al.  Study on models of single populations , 1982 .

[11]  Tzy-Wei Hwang,et al.  Global analysis of the predator–prey system with Beddington–DeAngelis functional response , 2003 .

[12]  J. Vandermeer,et al.  Indirect effects with a keystone predator: coexistence and chaos. , 1998, Theoretical population biology.

[13]  Zhenqing Li,et al.  The dynamics of a Beddington-type system with impulsive control strategy☆ , 2006 .

[14]  Vikas Rai,et al.  Chaotic population dynamics and biology of the top-predator , 2004 .

[15]  M. A. Aziz-Alaoui,et al.  Study of a Leslie–Gower-type tritrophic population model , 2002 .

[16]  G C Sabin,et al.  Chaos in a periodically forced predator-prey ecosystem model. , 1993, Mathematical biosciences.

[17]  Sunita Gakkhar,et al.  Seasonally perturbed prey–predator system with predator-dependent functional response , 2003 .

[18]  Vikas Rai,et al.  Crisis-limited chaotic dynamics in ecological systems , 2001 .

[19]  Ranjit Kumar Upadhyay,et al.  Effect of seasonality on the dynamics of 2 and 3 species prey-predator systems , 2005 .

[20]  Lee A. Segel,et al.  Modeling Dynamic Phenomena in Molecular and Cellular Biology , 1984 .

[21]  S. Rinaldi,et al.  Reduced order models for the prediction of the time of occurrence of extreme episodes , 2001 .

[22]  A Hastings,et al.  Chaos in one-predator, two-prey models: general results from bifurcation theory. , 1994, Mathematical biosciences.

[23]  Tzy-Wei Hwang,et al.  Uniqueness of limit cycles of the predator–prey system with Beddington–DeAngelis functional response , 2004 .

[24]  A. Hastings,et al.  Chaos in a Three-Species Food Chain , 1991 .

[25]  A. B. Peet,et al.  Complex dynamics in a three-level trophic system with intraspecies interaction. , 2005, Journal of theoretical biology.