Extending and generalizing the results of rational equations,
Dynamics of Third Order Rational Difference Equations with Open
Problems and Conjectures focuses on the boundedness nature of
solutions, the global stability of equilibrium points, the periodic
character of solutions, and the convergence to periodic solutions,
including their periodic trichotomies. The book also provides
numerous thought-provoking open problems and conjectures on the
boundedness character, global stability, and periodic behavior of
solutions of rational difference equations.
After introducing several basic definitions and general results,
the authors examine 135 special cases of rational difference
equations that have only bounded solutions and the equations that
have unbounded solutions in some range of their parameters. They
then explore the seven known nonlinear periodic trichotomies of
third order rational difference equations. The main part of the
book presents the known results of each of the 225 special cases of
third order rational difference equations. In addition, the
appendices supply tables that feature important information on
these cases as well as on the boundedness character of all fourth
order rational difference equations.
"A Framework for Future Research"
The theory and techniques developed in this book to understand
the dynamics of rational difference equations will be useful in
analyzing the equations in any mathematical model that involves
difference equations. Moreover, the stimulating conjectures will
promote future investigations in this fascinating, yet surprisingly
little known area of research.
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