Flip and Neimark–Sacker bifurcation in a differential equation with piecewise constant arguments model
| Autor: | Senol Kartal |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Period-doubling bifurcation
Algebra and Number Theory Differential equation Applied Mathematics 010102 general mathematics Mathematical analysis Saddle-node bifurcation Bifurcation diagram 01 natural sciences Nonlinear Sciences::Chaotic Dynamics 010101 applied mathematics Bifurcation theory Transcritical bifurcation Piecewise 0101 mathematics Analysis Center manifold Mathematics |
| Zdroj: | Journal of Difference Equations and Applications. 23:763-778 |
| ISSN: | 1563-5120 1023-6198 |
| DOI: | 10.1080/10236198.2016.1277214 |
| Popis: | In this paper, a differential equation with piecewise constant arguments model that describes a population density of a bacteria species in a microcosm is considered. The discretization process of a differential equation with piecewise constant arguments gives us two dimensional discrete dynamical system in the interval t∈[n,n+1). By using the center manifold theorem and the bifurcation theory, it is shown that the discrete dynamical system undergoes flip and Neimark–Sacker bifurcation. The bifurcation diagrams, phase portraits and Lyapunov exponents are obtained for the discrete model. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|