Basins of attraction of period-two solutions of monotone difference equations
| Autor: | Esmir Pilav, Arzu Bilgin, Mustafa R. S. Kulenović |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
education.field_of_study
Algebra and Number Theory Partial differential equation Differential equation Applied Mathematics 010102 general mathematics Mathematical analysis Population 01 natural sciences 010101 applied mathematics Nonlinear system Monotone polygon Ordinary differential equation Stability theory 0101 mathematics education Analysis Saddle Mathematics |
| Zdroj: | Advances in Difference Equations. 2016 |
| ISSN: | 1687-1847 |
| DOI: | 10.1186/s13662-016-0801-y |
| Popis: | We investigate the global character of the difference equation of the form $$x_{n+1} = f(x_{n}, x_{n-1}),\quad n=0,1, \ldots $$ with several period-two solutions, where f is increasing in all its variables. We show that the boundaries of the basins of attractions of different locally asymptotically stable equilibrium solutions or period-two solutions are in fact the global stable manifolds of neighboring saddle or non-hyperbolic equilibrium solutions or period-two solutions. As an application of our results we give the global dynamics of three feasible models in population dynamics which includes the nonlinearity of Beverton-Holt and sigmoid Beverton-Holt types. |
| Databáze: | OpenAIRE |
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