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1 results

  • GLOBAL ASYMPTOTIC STABILITY FOR GENERAL SYMMETRIC RATIONAL DIFFERENCE EQUATIONS

  • Part of
  • CONG ZHANG, HONG-XU LI, NAN-JING HUANG
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 81 / Issue 2 / April 2010
    Published online by Cambridge University Press:
    02 October 2009, pp. 251-259
    Print publication:
    April 2010
    • Article
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  • We investigate the global asymptotic stability for positive solutions to a class of general symmetric rational difference equations and prove that the unique positive equilibrium 1 of the general symmetric rational difference equations is globally asymptotically stable. As a special case of our result, we solve the conjecture raised by Berenhaut, Foley and Stević [‘The global attractivity of the rational difference equation yn=(yn−k+yn−m)/(1+yn−kyn−m)’, Appl. Math. Lett.20 (2007), 54–58].