It is proposed and studied a prey-predator system with a Holling type II functional response that merges predation fear with a predator-dependent prey's refuge. Understanding the impact of fear and refuge on the system's dynamic behavior is one of the objectives. All conceivable steady-states are investigated for their stability. The persistence condition of the system has been established. Local bifurcation analysis is performed in the Sotomayor sense. Extensive numerical simulation with varied parameters was used to explore the system's global dynamics. A limit cycle and a point attractor are the two types of attractors in the system. It's also interesting to note that the system exhibits bi-stability between these 2 types of attractors.

In this paper, the conditions of persistence of a mathematical model, consists from
a predator interacting with stage structured prey are established. The occurrence of
local bifurcation and Hopf bifurcation are investigated. Finally, in order to confirm
our obtained analytical results, numerical simulations have been done for a
hypothetical set of parameter values .

This paper examines a new nonlinear system of multiple integro-differential equations containing symmetric matrices with impulsive actions. The numerical-analytic method of ordinary differential equations and Banach fixed point theorem are used to study the existence, uniqueness and stability of periodic solutions of impulsive integro-differential equations with piecewise continuous functions. This study is based on the Hölder condition in which the ordering ,  and  are real numbers between 0 and 1.

    First principle calculations are performed to theoretically predict the physical properties of hexagonal aluminium arsenide planar and buckled monolayers. The structural characteristics showed that the buckled parameter is about 0.32 A°. Cohesive energies have favourable values and it indicates the fabrication possibility. Phonon dispersion properties indicated that the planar aluminium arsenic monolayers are dynamically unstable, while the buckled is less dynamically unstable. The elastic constant parameters achieved the required characteristics of stable hexagonal monolayer structures. The study of electronic band structure prefers to indirect semiconductor band gaps, and the density of states showed strong orbital hybridizati

In this paper a mathematical model that describes the flow of infectious disease in a population is proposed and studied. It is assumed that the disease divided the population into four classes: susceptible individuals (S), vaccinated individuals (V), infected individuals (I) and recover individuals (R). The impact of immigrants, vaccine and external sources of disease, on the dynamics of SVIRS epidemic model is studied. The existence, uniqueness and boundedness of the solution of the model are discussed. The local and global stability of the model is studied. The occurrence of local bifurcation as well as Hopf bifurcation in the model is investigated. Finally the global dynamics of the proposed model is studied numerically.

    The electronic properties (such as energy gap HOMO levels. LUMO levels, density of state and density of bonds in addition to spectroscopic properties like IR spectra, Raman spectra, force constant and reduced masses as a function of frequency) of coronene C₂₄ and reduced graphene oxide C₂₄O_X , where x=1-5, were studied.. The  methodology employed was  Density Functional Theory (DFT) with Hybrid function B3LYP and 6-311G** basis sets. The energy gap was calculated for C₂₄ to be 3.5 eV and for C₂₄O_x was from 0.89 to 1.6862 eV  for x=1-5 ,respectively.   These energy gaps values are comparable to the measured gap of Graphene (1-2.2 eV). The spectroscopic propertie

    The electronic properties (such as energy gap HOMO levels. LUMO levels, density of state and density of bonds in addition to spectroscopic properties like IR spectra, Raman spectra, force constant and reduced masses as a function of frequency) of coronene C24 and reduced graphene oxide C24OX , where x=1-5, were studied.. The  methodology employed was  Density Functional Theory (DFT) with Hybrid function B3LYP and 6-311G** basis sets. The energy gap was calculated for C24 to be 3.5 eV and for C24Ox was from 0.89 to 1.6862 eV  for x=1-5 ,respectively.   These energy gaps values are comparable to the measured gap of Graphene (1-2.2 eV). The spectroscopic properties were  compared with experimental measurements, specificall

this paper give a proof of known conditions for the existence of peridic conincidence points of continuius maps using lindemann theotem on transcendental numbers

Ajloun reserve is the most important reserved areas set up by the Jordanian government to encourage development and ecotourism, is located on the green mountains of Ajloun north of Jordan, was founded in 1989 and follow The Royal Society for the conservation of the natur, an area of 13 km2, and covered with thick forests of oak trees and Butm, maple and others, characterized by the diversity of vital consists of 319 species of medicinal and aromatic plants and wild flowers, and where there are 40 species of birds, 14 species of mammals, 16 reptiles, 5 species of plants registered in the world. The Reserve has a great importance in Jordan ,it is the most reservations attractive to tourists, both internally and externally, and prov