In this paper, a mathematical model consisting of harmful phytoplankton and two competing zooplankton is proposed and studied. The existence of all possible equilibrium points is carried out. The dynamical behaviors of the model system around biologically feasible equilibrium points are studied. Suitable Lyapunov functions are used to construct the basins of attractions of those points. Conditions for which the proposed model persists are established. The occurrence of local bifurcation and a Hopf bifurcation are investigated. Finally, to confirm our obtained analytical results and specify the vital parameters, numerical simulations are used for a hypothetical set of parameter values.

An expression for the transition charge density is investigated where the deformation in nuclear collective modes is taken into consideration besides the shell model transition density. The inelastic longitudinal form factors C2 calculated using this transition charge density with excitation of the levels for Cr54,52,50 nuclei. In this work, the core polarization transition density is evaluated by adopting the shape of Tassie model together with the derived form of the ground state two-body charge density distributions (2BCDD's). It is noticed that the core polarization effects which represent the collective modes are essential in obtaining a remarkable agreement between the calculated inelastic longitudinal F(q)'s and those of experimen

The aim of this article, we define new iterative methods called three-step type in which Jungck resolvent CR-iteration and resolvent Jungck SP-iteration are discussed and study rate convergence and strong convergence in Banach space to reach the fixed point which is differentially solve of nonlinear equations. The studies also expanded around it to find the best solution for nonlinear operator equations in addition to the varying inequalities in Hilbert spaces and Banach spaces, as well as the use of these iterative methods to approximate the difference between algorithms and their images, where we examined the necessary conditions that guarantee the unity and existence of the solid point. Finally, the results show that resolvent CR-iter

       In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

       This paper treats the interactions among four population species. The system includes one mutuality prey, one harvested prey and two predators. The four species interaction can be described as a food chain, where the first prey helps the second harvested prey. The first and the second predator attack the first and the second prey, respectively, according to Lotka-Volterra type functional responses. The model is formulated using differential equations. One equilibrium point of the model is found and analysed to reveal a threshold that will allow the coexistence of all species. All other equilibrium points of the system are located, with their local and global stability being assessed. To back up the conclusions of the mathema

This study deals with the absence of state control over the whole of the Syrian geography in creating an environment conducive to the emergence of a new force represented by armed groups and organizations that point to fundamental changes in the conflict and to transform competition for control over the land into a struggle for influence. Which in itself represents the prospects of change in the Syrian scene, and that understanding their interests requires shedding light on the extent of the continuation of this competition and the conflict on land and expansion at the expense of the other, and thus contribute to complicate the Syrian scene, especially after attempts to bite Of land and annexation to each party's areas of influence, espe

In this work, the external switching dynamics of a Fabry-Perot etalon are studied via optical bistability system simulation. The simulated set-up of this investigation consists of two laser beams; the first beam is continuous (CW) which is considered as a biasing beam and capable of holding the bistable system for a certain range, which we are interested in, from a point that is very close self-switching to a point where the switching is unachievable. The second beam is modulated by passing the first beam through an acousto-optic modulator (AOM) to produce pulses with a minimum rise time and is used as an external source (coherent switching). In this work, we obtained the optical bistable loops by applying absorption coefficient (α) =

The dynamics of a single condensing two-phase bubble of two different dispersed-continuous systems were studied. The systems were, CCl₄ - water and CCl₄ - 100% glycerol. Cinephotography was used to determine the change in height, diameter and time. These results were used to determine the experimental rise velocity of the bubble, which was compared with a theoretical one based on some equations used. It was found that the velocity of the first system remained almost constant, while it decreased gradually for the second system.