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This paper deals with a delayed single population model on time scales. With the assistance of coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Furthermore, the better estimations for bounds of periodic solutions are established. Keywords—Coincidence degree, continuation theorem, periodic solutions, time… (More)
In this paper, the semi–ratio–dependent predator-prey system with nonmonotonic functional response on time scales is investigated. By using the coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Keywords—Semi–ratio–dependent, predator–prey system, coincidence degree, time scales.
By incorporating a prey refuge, this paper proposes new discrete Leslie–Gower predator–prey systems with and without Allee effect. The existence of fixed points are established and the stability of fixed points are discussed by analyzing the modulus of characteristic roots. Keywords—Leslie–Gower; predator–prey model; prey refuge; Allee effect.
In this paper, a delayed SIS (Susceptible Infectious Susceptible) model with stage structure is investigated. We study the Hopf bifurcations and stability of the model. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. The conditions to… (More)
In this paper, by using the Mawhin’s continuation theorem, we prove the existence of periodic solutions for a stage-structure ecological model on time scales. This unifies the results for differential and difference equations.
The main purpose of this paper is to investigate a discrete time three–species food chain system with ratio dependence. By employing coincidence degree theory and analysis techniques, sufficient conditions for existence of periodic solutions are established. Keywords—Food chain; ratio–dependent; coincidence degree; periodic solutions
In this paper, a delay model of plankton allelopathy is investigated. By using the coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. The presented criteria improve and extend previous results in the literature. 2000 Mathematics Subject Classification: 92D25, 34C25.
With the help of coincidence degree theory, sufficient conditions for existence of periodic solutions for a food chain model with functional responses on time scales are established. Keywords—time scales, food chain model, coincidence degree, periodic solutions.
Abstract: Viruses have important influences on human health: they not only cause some common diseases, but also cause serious illnesses. Moreover, the conventional medicines usually fail to prevent or treat them, and viral infections are hard to treat because viruses live inside the body’s cells. However, some mathematical models can help to understand the… (More)
Evaluation is an essential step in the process of the design and development of a computer game system. By it, the defect of the system can be found immediately. So it directly decides the quality of a computer game. In the evaluation of the computer games, Usability Evaluation is a core content. Being lack of the relative theory and practice in China… (More)