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Stability of Real Parametric Polynomial Discrete Dynamical Systems
Joint Authors
Solís Lozano, Francisco
Franco-Medrano, Fermin
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-02-15
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter λ and generalize this characterization to cubic real polynomial maps, in a consistent theory that is further generalized to real mth degree real polynomial maps.
In essence, we give conditions for the stability of the fixed points of any real polynomial map with real fixed points.
In order to do this, we have introduced the concept of canonical polynomial maps which are topologically conjugate to any polynomial map of the same degree with real fixed points.
The stability of the fixed points of canonical polynomial maps has been found to depend solely on a special function termed Product Position Function for a given fixed point.
The values of this product position determine the stability of the fixed point in question, when it bifurcates and even when chaos arises, as it passes through what we have termed stability bands.
The exact boundary values of these stability bands are yet to be calculated for regions of type greater than one for polynomials of degree higher than three.
American Psychological Association (APA)
Franco-Medrano, Fermin& Solís Lozano, Francisco. 2015. Stability of Real Parametric Polynomial Discrete Dynamical Systems. Discrete Dynamics in Nature and Society،Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1060725
Modern Language Association (MLA)
Franco-Medrano, Fermin& Solís Lozano, Francisco. Stability of Real Parametric Polynomial Discrete Dynamical Systems. Discrete Dynamics in Nature and Society No. 2015 (2015), pp.1-13.
https://search.emarefa.net/detail/BIM-1060725
American Medical Association (AMA)
Franco-Medrano, Fermin& Solís Lozano, Francisco. Stability of Real Parametric Polynomial Discrete Dynamical Systems. Discrete Dynamics in Nature and Society. 2015. Vol. 2015, no. 2015, pp.1-13.
https://search.emarefa.net/detail/BIM-1060725
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1060725