Global behaviour of a predator–prey like model with piecewise constant arguments
| Autor: | Senol Kartal, Fuat Gürcan |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Lyapunov function
Ecology Differential equation Population Dynamics Mathematical analysis Models Biological Stability (probability) symbols.namesake Predatory Behavior Limit cycle Stability theory symbols Piecewise Animals Constant (mathematics) Algorithms Ecosystem Ecology Evolution Behavior and Systematics Bifurcation Mathematics |
| Zdroj: | Journal of Biological Dynamics. 9:159-171 |
| ISSN: | 1751-3766 1751-3758 |
| DOI: | 10.1080/17513758.2015.1049225 |
| Popis: | The present study deals with the analysis of a predator-prey like model consisting of system of differential equations with piecewise constant arguments. A solution of the system with piecewise constant arguments leads to a system of difference equations which is examined to study boundedness, local and global asymptotic behaviour of the positive solutions. Using Schur-Cohn criterion and a Lyapunov function, we derive sufficient conditions under which the positive equilibrium point is local and global asymptotically stable. Moreover, we show numerically that periodic solutions arise as a consequence of Neimark-Sacker bifurcation of a limit cycle. |
| Databáze: | OpenAIRE |
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