In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynami

Robot manipulator is a multi-input multi-output system with high complex nonlinear dynamics, requiring an advanced controller in order to track a specific trajectory. In this work, forward and inverse kinematics are presented based on Denavit Hartenberg notation to convert the end effector planned path from cartesian space to joint space and vice versa where a cubic spline interpolation is used for trajectory segments to ensure the continuity in velocity and acceleration.  Also, the derived mathematical dynamic model is based on Eular Lagrange energy method to contain the effect of friction and disturbance torques beside the inertia and Coriolis effect. Two types of controller are applied ; the nonlinear computed torque control (CTC

Experiments research is done to determine how saturated stiff clayey soil responds to a single impulsive load. Models made of saturated, stiff clay were investigated. To supply the single pulse energy, various falling weights from various heights were tested using the falling weight deflectometer (FWD). Dynamic effects can range from the major failure of a sensitive sensor or system to the apparent destruction of structures. This study examines the response of saturated stiff clay soil to a single impulsive load (vertical displacement at the soil surface below and beside the bearing plates). Such reactions consist of displacements, velocities, and accelerations caused by the impact occurring at the surface depth induced by the impact loads

Background: The need of the patient for a more reasonable esthetic orthodontic intervention has risen nowadays. Thus, orthodontists make use of esthetic orthodontic materials like brackets, ligature elastics, and arch wires. The esthetic brackets come as different forms of materials, such as ceramic brackets, which have their stainability remaining as the most important consideration for the patients and the orthodontists. This study aimed to compare the staining effects of various staining materials, including black tea, cigarette smoke and Pepsi, as well as the time effect on the color stability of sapphire ceramic brackets bonded with three kinds of light cure orthodontic adhesives: Transbond, Resilience and Enlight. Materials and Met

The main objective of this research is to find the coefficient of permeability (k) of the soil and especially clayey soil by finding the degree of consolidation (rate of consolidation). New modify procedure is proposed by using the odometer (consolidation) device. The ordinary conventional permeability test usually takes a long time by preparing and by testing and this could cause some problems especially if there is a need to do a large number of this test and there were a limited number of technicians and/or apparatus. From this point of view the importance of this research is clear, since the modified procedure will require a time of 25 minute only. Derivation made to produce an equation which could be used to fined the permeabi

In this work, a single pile is physically modeled and embedded in an upper liquefiable loose sand layer overlying a non-liquefiable dense layer. A laminar soil container is adopted to simulate the coupled static-dynamic loading pile response during earthquake motions: Ali Algharbi, Halabjah, El-Centro, and Kobe earthquakes. During seismic events with combined loading, the rotation along the pile, the lateral and vertical displacements at the pile head as well as the pore pressure ratio in loose sandy soil were assessed. According to the experimental findings, combined loading that ranged from 50 to 100% of axial load would alter the pile reaction by reducing the pile head peak ground acceleration, rotation of the pile, and lateral displacem

This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a thir

This paper proposes a new method to tune a fractional order PID controller. This method utilizes both the analytic and numeric approach to determine the controller parameters. The control design specifications that must be achieved by the control system are gain crossover frequency, phase margin, and peak magnitude at the resonant frequency, where the latter is a new design specification suggested by this paper. These specifications results in three equations in five unknown variables. Assuming that certain relations exist between two variables and discretizing one of them, a performance index can be evaluated and the optimal controller parameters that minimize this performance index are selected. As a case study, a third order linear time

Let f and g be a self – maps of a rational exterior space . A natural number m is called a minimal coincidence period of maps f and g if f^m and g^m have a coincidence point which is not coincidence by any earlier iterates. This paper presents a complete description of the set of algebraic coincidence periods for self - maps of a rational exterior space which has rank 2 .