2008
DOI: 10.1080/10236190701761482
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On second-order rational difference equations, Part 2

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Cited by 34 publications
(46 citation statements)
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“…In a special case when equation (2) has three equilibrium solutions and all solutions are asymptotic to one of these equilibrium solutions only partial description of the basins of attraction of these equilibrium solutions was given in [1,2]. Here we improve these results by obtaining the complete description of the basins of attraction of all equilibrium solutions.…”
Section: Introductionmentioning
confidence: 84%
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“…In a special case when equation (2) has three equilibrium solutions and all solutions are asymptotic to one of these equilibrium solutions only partial description of the basins of attraction of these equilibrium solutions was given in [1,2]. Here we improve these results by obtaining the complete description of the basins of attraction of all equilibrium solutions.…”
Section: Introductionmentioning
confidence: 84%
“…which was considered in [1,2] and some precise results on global dynamics were obtained. In a special case when equation (2) has three equilibrium solutions and all solutions are asymptotic to one of these equilibrium solutions only partial description of the basins of attraction of these equilibrium solutions was given in [1,2].…”
Section: Introductionmentioning
confidence: 98%
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“…and the result follows by employing Theorem 1.6 in[1]. Clearly, one can see that the component {y n } of the solution is bounded.…”
mentioning
confidence: 84%
“…Note that even if the system trajectory lies out of region (22) initially, (2) and (15) ensure that the trajectory will enter region (22) and will not leave this region once it enters. In other words, for our present objective of arriving at the global asymptotic stability result, the initial condition may be assumed to be such as to satisfy (22).…”
Section: State-space Criterionmentioning
confidence: 98%