161
Views
5
CrossRef citations to date
0
Altmetric
Articles

Basins of attraction of equilibrium and boundary points of second-order difference equations

&
Pages 947-959 | Received 06 May 2013, Accepted 05 Oct 2013, Published online: 22 Nov 2013

REFERENCES

  • A.M.Amleh, E.Camouzis, and G.Ladas, On the dynamics of a rational difference equation, part I, Int. J. Differ. Equ.3 (2008), pp. 1–35.
  • A.M.Amleh, E.Camouzis, and G.Ladas, On the dynamics of a rational difference equation, part II, Int. J. Differ. Equ.3 (2008), pp. 1–30.
  • A.Brett and M.R.S.Kulenović, Basins of attraction of equilibrium points of monotone difference equations, Sarajevo J. Math.5 (2009), pp. 211–233.
  • E.Camouzis, M.R.S.Kulenović, O.Merino, and G.Ladas, Rational systems in the plane, J. Differ. Equ. Appl.15 (2009), pp. 303–323.
  • E.Camouzis and G.Ladas, Dynamics of Third-Order Rational Difference Equations: With Open Problems and Conjectures, Chapman & Hall/CRC Press, Boca Raton, FL, November2007.
  • P.de Mottoni and A.Schiaffino, Competition systems with periodic coefficients: A geometric approach, J. Math. Biol.11 (1981), pp. 319–335.
  • E.G.Enciso and E.D.Sontag, Global attractivity, I/O monotone small-gain theorems, and biological delay systems, Discrete Contin. Dyn. Syst.14 (2006), pp. 549–578.
  • M.Garić-Demirović, M.R.S.Kulenović, and M.Nurkanović, Basins of attraction of equilibrium points of second order difference equations, Appl. Math. Lett.25 (2012), pp. 2110–2115.
  • M.Hirsch and H.L.Smith, Monotone maps: A review, J. Differ. Equ. Appl.11 (2005), pp. 379–398.
  • E.Janowski and M.R.S.Kulenović, Attractivity and global stability for linearizable difference equations, Comput. Math. Appl.57 (2009), pp. 1592–1607.
  • S.Kalabušić, M.R.S.Kulenović, and E.Pilav, Global dynamics of a competitive system of rational difference equations in the plane, Adv. Differ. Equ. (2009), Art. ID 132802, 30 pp.
  • S.Kalabušić, M.R.S.Kulenović, and E.Pilav, Dynamics of a two-dimensional system of rational difference equations of Leslie-Gower type, Adv. Differ. Equ. (2011), 29 pp.
  • C.M.Kent and H.Sedaghat, Global attractivity in a quadratic-linear rational difference equation with delay, J. Differ. Equ. Appl.15 (2009), pp. 913–925.
  • C.M.Kent and H.Sedaghat, Global attractivity in a rational delay difference equation with quadratic terms, J. Differ. Equ. Appl.17 (2011), pp. 457–466.
  • M.R.S.Kulenović and G.Ladas, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman and Hall/CRC, Boca Raton/London, 2001.
  • M.R.S.Kulenović and O.Merino, Discrete Dynamical Systems and Difference Equations with Mathematica, Chapman and Hall/CRC, Boca Raton/London, 2002.
  • M.R.S.Kulenović and O.Merino, A global attractivity result for maps with invariant boxes, Discrete Contin. Dyn. Syst. Ser.B6 (2006), pp. 97–110.
  • M.R.S.Kulenović and O.Merino, Competitive-exclusion versus competitive-coexistence for systems in the plane, Discrete Contin. Dyn. Syst. Ser.B6 (2006), pp. 1141–1156.
  • M.R.S.Kulenović and O.Merino, Global bifurcations for competitive systems in the plane, Discrete Contin. Dyn. Syst. Ser.B12 (2009), pp. 133–149.
  • M.R.S.Kulenović and O.Merino, Invariant manifolds for competitive discrete systems in the plane, Int. J. Bifur. Chaos20 (2010), pp. 2471–2486.
  • M.R.S.Kulenović and M.Nurkanović, Asymptotic behavior of a linear fractional system of difference equations, J. Ineq. Appl. (2005), pp. 127–144.
  • M.R.S.Kulenović and M.Nurkanović, Asymptotic behavior of a competitive system of linear fractional difference equations, Adv. Differ. Equ., Art. ID 19756, 13 pp (2006)
  • M.R.S.Kulenović and A.-A.Yakubu, Compensatory versus overcompensatory dynamics in density-dependent Leslie models, J. Differ. Equ. Appl.10 (2004), pp. 1251–1265.
  • H.Sedaghat, Nonlinear Difference Equations: Theory with Applications to Social Science Models. Mathematical Modelling: Theory and Applications, Vol. 15, Kluwer Academic Publishers, Dordrecht, 2003.
  • H.Sedaghat, Global behaviours of rational difference equations of orders two and three with quadratic terms, J. Differ. Equ. Appl.15 (2009), pp. 215–224.
  • H.L.Smith, Periodic competitive differential equations and the discrete dynamics of competitive maps, J. Differ. Equ.64 (1986), pp. 165–194.
  • H.L.Smith, Planar competitive and cooperative difference equations, J. Differ. Equ. Appl.3 (1998), pp. 335–357.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.