In this paper, the effects of prey’s fear on the dynamics of the prey, predator, and scavenger system incorporating a prey refuge with the linear type of functional response were studied theoretically as well as numerically approach. The local and global stabilities of all possible equilibrium points are investigated. The persistence conditions of the model are established. the local bifurcation analysis around the equilibrium points, as well as the Hopf bifurcation near the positive equilibrium point, are discussed and analyzed. Finally, numerical simulations are carried out, and the obtained trajectories are drowned using the application of Matlab version (6) to explain our found analytical

An eco-epidemic model is proposed in this paper. It is assumed that there is a stage structure in prey and disease in predator. Existence, uniqueness and bounded-ness of the solution for the system are studied. The existence of each possible steady state points is discussed. The local condition for stability near each steady state point is investigated. Finally, global dynamics of the proposed model is studied numerically.

    Our aim in this work is to study the classical continuous boundary control vector  problem for triple nonlinear partial differential equations of elliptic type involving a Neumann boundary control. At first, we prove that the triple nonlinear partial differential equations of elliptic type with a given classical continuous boundary control vector have a unique "state" solution vector,  by using the Minty-Browder Theorem. In addition, we prove the existence of a classical continuous boundary optimal control vector ruled by the triple nonlinear partial differential equations of elliptic type with equality and inequality constraints. We study the existence of the unique solution for the triple adjoint equations

In this study, the performance of the adaptive optics (AO) system was analyzed through a numerical computer simulation implemented in MATLAB. Making a phase screen involved turning computer-generated random numbers into two-dimensional arrays of phase values on a sample point grid with matching statistics. Von Karman turbulence was created depending on the power spectral density. Several simulated point spread functions (PSFs) and modulation transfer functions (MTFs) for different values of the Fried coherent diameter (r_o) were used to show how rough the atmosphere was. To evaluate the effectiveness of the optical system (telescope), the Strehl ratio (S) was computed. The compensation procedure for an AO syst

In this paper, an approximate solution of nonlinear two points boundary variational problem is presented. Boubaker polynomials have been utilized to reduce these problems into quadratic programming problem. The convergence of this polynomial has been verified; also different numerical examples were given to show the applicability and validity of this method.

تناول البحث حل مشكلة النقل باستخدام مدخل بحوث العملٌات فً مرحلة التحلٌل والتصمٌم لنموذج المشكلة , وتم مقارنة النتائج التً حصلنا علٌها من الحلول لصٌاؼة التحلٌل وبرهنة صحة النموذج المتجه صوب الموضوع, وتم اجراء المقارنة بٌن الحلول المختلفة الختٌار اقل قٌمة لدالة الهدؾ لكً ٌتمكن المستفٌد من صنع القرار, باستخدام الطرق االربعة )طرٌقة الزاوٌة الشمالٌة الؽربٌة, طرٌقة اقل التكالٌؾ, طرٌقة فوجل التقرٌبٌة, الطرٌقة ال

Buckling analysis of a laminated composite thin plate with different boundary conditions subjected to in-plane uniform load are studied depending on classical laminated plate theory; analytically using (Rayleigh-Ritz method). Equation of motion of the plates was derived using the principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. The eigenvalue problem generated by using Ritz method, the set of linear algebraic equations can be solved using MATLAB for symmetric and anti-symmetric, cross and angle-ply laminated plate considering some design parameters such as aspect ratios, number of layers, lamination type and orthotropic ratio. The results obtained g

This paper introduces a non-conventional approach with multi-dimensional random sampling to solve a cocaine abuse model with statistical probability. The mean Latin hypercube finite difference (MLHFD) method is proposed for the first time via hybrid integration of the classical numerical finite difference (FD) formula with Latin hypercube sampling (LHS) technique to create a random distribution for the model parameters which are dependent on time [Formula: see text]. The LHS technique gives advantage to MLHFD method to produce fast variation of the parameters’ values via number of multidimensional simulations (100, 1000 and 5000). The generated Latin hypercube sample which is random or non-deterministic in nature is further integ