Contemporary Methods in Mathematical Physics and Gravitation

55-70

Authors: T. Donchev, A. Nosheen, R. Ahmed

In this paper we investigate ordinary fuzzy differential inclusions. Using compactness type conditions we prove main results for the existence of solutions. We prove that the solution set is Rδ extending the classical Kneser’s theorem.

15

Authors: Qamar Din

We study the qualitative behavior of a predator-prey model, where the carrying capacity of the predators environment is proportional to the number of prey. We investigate the boundedness character, steady-states, local asymptotic stability of equilibrium points, and global behavior of the unique positive equilibrium point of a discrete predator-prey model given by \begin{equation*} x_{n+1}=\frac{\alpha x_n-\beta x_n y_n}{1+ \gamma x_n},\ y_{n+1}=\frac{\delta x_ny_n}{x_n+\eta y_n}, \end{equation*} where parameters α, β, γ, δ, η and initial conditions are positive real numbers. Moreover, the rate of convergence of positive solutions is also discussed. Some numerical examples are given to verify our theoretical results.