Uniform ultimate boundedness of solutions of predator-prey system with Michaelis-Menten functional response on time scales. (English) Zbl 1418.92148
Summary: In this paper, a predator-prey system with Michaelis-Menten functional response on time scales is investigated. First of all, we generalize the semi-cycle concept to time scales. Second, we obtain the uniformly ultimate boundedness of solutions of this system. Our results demonstrate that when the death rate of the predator is rather small without prey, whereas the intrinsic growth rate of the prey is relatively large, the species could coexist in the long run. In particular, if \(\mathbb{T}=\mathbb{R}\) or \(\mathbb{T}=\mathbb{Z}\), some well-known results have been generalized. In addition, for the continuous case, we provide a new idea to prove its permanence. Finally, a numerical simulation is given to support our main results.
MSC:
| 92D25 | Population dynamics (general) |
| 34N05 | Dynamic equations on time scales or measure chains |
| 37N25 | Dynamical systems in biology |
Keywords:
\(\omega\)-periodic solutions; uniform ultimate boundedness; semi-cycle; time scales; predator-prey systemReferences:
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