Global dynamics of cubic second order difference equation in the first quadrant

Citation data:

Advances in Difference Equations, ISSN: 1687-1847, Vol: 2015, Issue: 1, Page: 176

Publication Year:
2015
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Repository URL:
http://digitalcommons.uri.edu/math_facpubs/15; https://digitalcommons.uri.edu/cgi/viewcontent.cgi?article=1014&context=math_facpubs
DOI:
10.1186/s13662-015-0503-x
Author(s):
Bektešević, Jasmin; Kulenović, Mustafa RS; Pilav, Esmir
Publisher(s):
Springer Nature; DigitalCommons@URI
Tags:
Mathematics
article description
We investigate the global behavior of a cubic second order difference equation (Formula presented.) , with nonnegative parameters and initial conditions. We establish the relations for the local stability of equilibriums and the existence of period-two solutions. We then use this result to give global behavior results for special ranges of the parameters and determine the basins of attraction of all equilibrium points. We give a class of examples of second order difference equations with quadratic terms for which a discrete version of the 16th Hilbert problem does not hold. We also give the class of second order difference equations with quadratic terms for which the Julia set can be found explicitly and represent a planar quadratic curve.