Study of the stability of a 3×3 system of difference equations using Centre Manifold Theory
| Autor: | Nikolaos Psarros, C. J. Schinas, Garyfalos Papaschinopoulos |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Applied Mathematics
010102 general mathematics Mathematical analysis Zero (complex analysis) Analytical chemistry System of difference equations Absolute value (algebra) 01 natural sciences Stability (probability) 010101 applied mathematics Centre manifold 0101 mathematics Eigenvalues and eigenvectors Real number Mathematics |
| Zdroj: | Applied Mathematics Letters. 64:185-192 |
| ISSN: | 0893-9659 |
| DOI: | 10.1016/j.aml.2016.09.002 |
| Popis: | We study the stability of the zero equilibrium of the following system of difference equations, which is a natural extension of an one-dimensional biologicalmodel: x n + 1 = a 1 x n + b 1 y n e − x n , y n + 1 = a 2 y n + b 2 z n e − y n , z n + 1 = a 3 z n + b 3 x n e − z n where a 1 , a 2 , a 3 , b 1 , b 2 , b 3 are real constants and the initial values conditions x 0 , y 0 and z 0 are real numbers. The stability of those systems in the special case when one of the eigenvalues has absolute value equal to 1 and the other two eigenvalues have absolute value less than 1, using centre manifold theory, is investigated. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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