The dynamical behavior of a two-dimensional continuous time dynamical system describing by a prey predator model is investigated. By means of constructing suitable Lyapunov functional, sufficient condition is derived for the global asymptotic stability of the positive equilibrium of the system. The Hopf bifurcation analysis is carried out. The numerical simulations are used to study the effect of periodic forcing in two different parameters. The results of simulations show that the model under the effects of periodic forcing in two different parameters, with or without phase difference, could exhibit chaotic dynamics for realistic and biologically feasible parametric values.

This  research  involves  studying  the  influence  of  increasing  the

number of Gaussian points and the style of their distribution, on a circular exit pupil, on the numerical calculations accuracy of the point spread function for an ideal optical system and another system having focus error of (0.25 A. and 0.5 A. )

It was shown that the accuracy of the results depends on the type of

distributing points on the exit pupil. Also, the accuracy increases with the increase of the number of points (N) and the increase of aberrations which requires on increas (N).

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 paper We introduce some new types of almost bi-periodic points in topological bitransfprmation groups and thier effects on some types of minimaliy in topological dynamics

This paper presents the Extended State Observer (ESO) based repetitive control (RC) for piezoelectric actuator (PEA) based nano-positioning systems. The system stability is proved using Linear Matrix Inequalities (LMIs), which guarantees the asymptotic stability of the system. The ESObased RC used in this paper has the ability to eliminate periodic disturbances, aperiodic disturbances and model uncertainties. Moreover, ESO can be tuned using only two parameters and the model free approach of ESO-based RC, makes it an ideal solution to overcome the challenges of nano-positioning system control. Different types of periodic and aperiodic disturbances are used in simulation to demonstrate the effectiveness of the algorithm. The comparison studi

The aim of this paper is to design fast neural networks to approximate periodic functions, that is, design a fully connected networks contains links between all nodes in adjacent layers which can speed up the approximation times, reduce approximation failures, and increase possibility of obtaining the globally optimal approximation. We training suggested network by Levenberg-Marquardt training algorithm then speeding suggested networks by choosing most activation function (transfer function) which having a very fast convergence rate for reasonable size networks.             In all algorithms, the gradient of the performance function (energy function) is used to determine how to

  The mind map represents a system to solve problems including design problems, because it depends on employing the complex and purposeful mental activity, which starts from a desire based on the search and investigation in order to reach integrated results of scientific thinking, utilizing the objective view of the scientific and practical aspects from various angles. This visual system can develop thinking and shorten the retrieval time of the previous information in order to employ it in the solution finding system, that it evokes past experiences and relates them to current situations, then enables the user to choose a suitable solution for the problems. This visual, educational and circulatory means, at the same time, has speci

The main objective of this study is to describe the preparation of topographic maps using the Surfer software. A total of 159 regularly distributed Ground Control Points (GCPs) were collected with the use of the Differential Global Positioning System (DGPS). Seven methods (Contour Map, Post Map, 3D Surface Map, 3D Wireframe Maps, Grid Vector-1 Map, Color Relief Map, and Shaded Relief Maps) at the Surfer environment were used to prepare the topographic maps at the Mukhtar Village near the Al-Fallujah City. Contour lines with other features were superimposed on the DEM layer, which refers to the topography of the terrain inside this study area. The accuracy of the database's results was estimated, essential maps were given, and the re

The current study involves placing 135 boreholes drilled to a depth of 10 m below the existing ground level. Three standard penetration tests (SPT) are performed at depths of 1.5, 6, and 9.5 m for each borehole. To produce thematic maps with coordinates and depths for the bearing capacity variation of the soil, a numerical analysis was conducted using MATLAB software. Despite several-order interpolation polynomials being used to estimate the bearing capacity of soil, the first-order polynomial was the best among the other trials due to its simplicity and fast calculations. Additionally, the root mean squared error (RMSE) was almost the same for the all of the tried models. The results of the study can be summarized by the production