Abstract
By means of special operators and operations, the so-called D-operators and the star-product, a special algebraic description for Nonlinear Polynomial Discrete Systems in two dimensions is developed. By using this description we can check if these nonlinear systems are “similar” or “equivalent” with linear systems, in the sense that the evolution of both systems, under the same initial conditions, are related to each other. Different kinds of solutions to the problem seem to determine different degrees of complexity for the original nonlinear systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
N. Karcanias, “Structure evolving systems and control in integrated design” Annual Reviews in Control 32 (2008) 161–182
S. Wiggins. Introduction to applied nonlinear dynamical systems and chaos. Springer-Verlag, New York, 1990.
Kotsios, S. and Lappas, D.1996. A description of 2-Dimensional discrete polynomial dynamics. IMA Journal of Mathematical Control and Information, Vol. 13, 409–428.
S.T.Glad (1989), “Differential algebraic modeling of nonlinear Systems”, In proceedings of MTNS-89, Amsterdam, 97–105.
S. Kotsios-D. Lappas “A Stability Result for “Separable” Nonlinear Discrete Systems.” IMA Journal of Mathematical Control and Information, 18, 325–339, (2001).
S. Kotsios “An Application on Ritt’s Remainder Algorithm to Discrete Polynomial Control Systems.” Journal of Mathematical Control and Information, 18, 19–29, (2001).
Stelios Kotsios - Dionyssios Lappas “The Nonlinearity of 2-D Discrete Systems. An Algebraic Approach.” Work in progress, (2013).
Stelios Kotsios, Dionyssios Lappas, “Linear Similarity of Nonlinear Polynomial Discrete Systems. An Algebraic Approach.” Conference of Modern Mathematical Methods in Science and Technology (M3ST), (2012), Kalamata, Greece.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Kotsios, S., Lappas, D. (2014). About Model Complexity of 2-D Polynomial Discrete Systems: An Algebraic Approach. In: Daras, N. (eds) Applications of Mathematics and Informatics in Science and Engineering. Springer Optimization and Its Applications, vol 91. Springer, Cham. https://doi.org/10.1007/978-3-319-04720-1_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-04720-1_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-04719-5
Online ISBN: 978-3-319-04720-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)