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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures (Paperback)
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Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures (Paperback)
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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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