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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 751594, 11 pages
http://dx.doi.org/10.1155/2013/751594
Research Article

Global Dynamics of Three Anticompetitive Systems of Difference Equations in the Plane

1Department of Mathematics, Rhode Island College, Providence, RI 02881-0816, USA
2Department of Mathematics, University of Rhode Island, Kingston, RI 02881-0816, USA

Received 11 September 2012; Revised 16 January 2013; Accepted 22 January 2013

Academic Editor: Raghib Abu-Saris

Copyright © 2013 M. DiPippo and M. R. S. Kulenović. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. S. Kalabušić and M. R. S. Kulenović, “Dynamics of certain anti-competitive systems of rational difference equations in the plane,” Journal of Difference Equations and Applications, vol. 17, no. 11, pp. 1599–1615, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. R. S. Kulenović and M. Nurkanović, “Basins of attraction of an anti-competitive system of difference equations in the plane,” Communications on Applied Nonlinear Analysis, vol. 19, no. 2, pp. 41–53, 2012. View at MathSciNet
  3. E. Camouzis, M. R. S. Kulenović, G. Ladas, and O. Merino, “Rational systems in the plane—open problems and conjectures,” Journal of Difference Equations and Applications, vol. 15, no. 3, pp. 303–323, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. D. Clark and M. R. S. Kulenović, “A coupled system of rational difference equations,” Computers & Mathematics with Applications, vol. 43, no. 6-7, pp. 849–867, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. P. Hess, Periodic-Parabolic Boundary Value Problems and Positivity, vol. 247 of Pitman Research Notes in Mathematics Series, Longman Scientific Technical, Harlow, UK; John Wiley & Sons, New York, NY, USA, 1991. View at MathSciNet
  6. M. W. Hirsch and H. Smith, “Monotone dynamical systems,” in Handbook of Differential Equations: Ordinary Differential Equations, vol. 2, pp. 239–357, Elsevier B. V., Amsterdam, The Netherlands, 2005. View at Zentralblatt MATH · View at MathSciNet
  7. M. R. S. Kulenović and O. Merino, Discrete Dynamical Systems and Difference Equations with Mathematica, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  8. M. R. S. Kulenović and M. Nurkanović, “Asymptotic behavior of a competitive system of linear fractional difference equations,” Advances in Difference Equations, vol. 2006, Article ID 19756, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Brett, M. Garić-Demirović, M. R. S. Kulenović, and M. Nurkanović, “Global behavior of two competitive rational systems of difference equations in the plane,” Communications on Applied Nonlinear Analysis, vol. 16, no. 3, pp. 1–18, 2009. View at Zentralblatt MATH · View at MathSciNet
  10. M. Garić-Demirović, M. R. S. Kulenović, and M. Nurkanović, “Global behavior of four competitive rational systems of difference equations in the plane,” Discrete Dynamics in Nature and Society, vol. 2009, Article ID 153058, 34 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. H. L. Smith, “Planar competitive and cooperative difference equations,” Journal of Difference Equations and Applications, vol. 3, no. 5-6, pp. 335–357, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. H. L. Smith, “The discrete dynamics of monotonically decomposable maps,” Journal of Mathematical Biology, vol. 53, no. 4, pp. 747–758, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. A. Brett and M. R. S. Kulenović, “Basins of attraction of equilibrium points of monotone difference equations,” Sarajevo Journal of Mathematics, vol. 5, pp. 211–233, 2009. View at Zentralblatt MATH · View at MathSciNet
  14. M. R. S. Kulenović and O. Merino, “Competitive-exclusion versus competitive-coexistence for systems in the plane,” Discrete and Continuous Dynamical Systems B, vol. 6, no. 5, pp. 1141–1156, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. M. R. S. Kulenović and O. Merino, “Global bifurcation for discrete competitive systems in the plane,” Discrete and Continuous Dynamical Systems B, vol. 12, no. 1, pp. 133–149, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. C. Robinson, Dynamical Systems: Stability, Symbolic Dynamics, and Chaos, CRC Press, Boca Raton, Fla, USA, 1995. View at MathSciNet
  17. C. A. Clark, M. R. S. Kulenović, and J. F. Selgrade, “On a system of rational difference equations,” Journal of Difference Equations and Applications, vol. 11, no. 7, pp. 565–580, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. M. R. S. Kulenović and O. Merino, “Invariant manifolds for competitive discrete systems in the plane,” International Journal of Bifurcation and Chaos, vol. 20, no. 8, pp. 2471–2486, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. E. Camouzis, G. Ladas, and L. Wu, “On the global character of the system xn+1=(α1+γ1yn)/(xn),yn+1=(β2xn+γ2yn)/(B2xn+C2yn),” International Journal of Pure and Applied Mathematics, vol. 53, no. 1, pp. 21–36, 2009. View at Zentralblatt MATH · View at MathSciNet
  20. Y. S. Huang and P. M. Knopf, “Global convergence properties of first-order homogeneous systems of rational difference equations,” Journal of Difference Equations and Applications, vol. 18, no. 10, pp. 1683–1707, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  21. M. R. S. Kulenović and G. Ladas, Dynamics of Second Order Rational Difference Equations: With Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2001. View at MathSciNet