Manuscript Topics

During the last eight decades there has been a great deal of activity in the study of discrete systems and especially in difference equations, when their solutions refer to problems generated in applied mathematics, such as statistics, biology, engineering, and other sciences. For instance, the investigation of the long-time behaviour of electric waves is greatly more simple by the use of difference equations. Besides the use of difference equations as approximations of ordinary and partial differential equations, they proved to be a powerful method for the study and analysis of problems in many applied systems, where there is a recurrence of states. In such cases some properties of the differential equations might not be inherited by the corresponding difference equation. Thus the big problem consists in suggesting the most appropriate approximation process which better describes the dynamics. However, having a recurrence process, one can express the solution in closed form, depending on known initial data, or, by the use of a computer simulation, one can predict the values of the solutions for huge values of time. This issue will focus on the latest achievements on all previous aspects of difference equations, especially on the dynamical behaviour of nonlinear difference equations and their applications.

Topics included, but not limited:
•  Difference equations generally,
•  Difference equations generated by ordinary differential equations and comparison of their solutions,
•  Solutions of Difference equations in closed form,
•  Qualitative properties, (e.g. stability, asymptotic stability, slowly varyingness, periodicity, almost periodicity, asymptotic periodicity),
•  Chaos in Lorenz-type discrete systems,
•  Asymptotic equivalence of Difference equations in general Banach Spaces.

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